Chapter 8 Opener Try It Yourself (p. 35). trapezoids. circles Large Perimeter Diameter Small Perimeter Diameter Average of Ratios 3. trapezoid, triangle. triangles 5. rectangle, triangle 6. rectangle, triangles. 5 5 5 5 8. a. b. 0 35 0 35 08 35 0 35 35 6 5 3.6 3. 3 3 3 9. ( ) 9 96 0. ( ) c. 0 35 0 35 3.. ( ) ( ) ( ) 3+ 8 39 3 9 9 3 8 3. ( + ) ( ) ( ) 3 3 0 3 0 0 3 00 3 00 88 Section 8. 8. Activity (pp. 36 3) Sides of Polygon Large Perimeter Diameter of Circle Small Perimeter. 0 mm 35 mm 00 mm d. The value of π is about 3., because this is the approximation given by the last row of the table. e. The calculations should have been more accurate, because a 96-sided polygon will look almost like the circle, so the perimeter should be a good approximation of the circumference. 3. Because π is equal to the circumference divided by the diameter, the circumference is equal to π times the diameter. So, to find the circumference, multiply the value of π by the diameter. A formula for the circumference is C πd. Sample answer: m Large Perimeter Diameter Small Perimeter Diameter Average of Ratios C πd The circumference is about meters. 0 35 Sides of Polygon 00 0 35 Large Perimeter 3.3 Diameter of Circle Small Perimeter. a. 6 0 mm 35 mm 08 mm b. 8 0 mm 35 mm 0 mm c. 0 0 mm 35 mm 0 mm. Answer should include, but is not limited to: Students should draw three circles using a compass. They should measure the diameter of each circle and use the formulas from Activity 3 to find the circumference of the circles. 8. On Your Own (pp. 38 30) d 6. r 8 The radius is 8 centimeters.. d r ( ) 9 8 The diameter is 8 yards. 3. C π r 3..56 The circumference is about.56 centimeters. 39
. C πd The circumference is about feet. 5. C πd 3. 9 8.6 The circumference is about 8.6 inches. 6. After the decrease, the diameter of the roll is 3. 5.5 6.5 inches. C πd 6.5 3. d 3d 9 d The diameter after the decrease is about 9 inches. C π d 3.. 3. So, the perimeter is about + 3. 5. feet. C πd 8. So, the perimeter is about + 8 centimeters. 9. C π r πr 3. 5. So, the perimeter is about ( 5) +.. inches. 8. Exercises (pp. 3 33) Vocabulary and Concept Check. The radius of a circle is one-half the diameter.. The phrase the distance from the center to any point on the circle does not belong because it describes the radius of a circle, and the other three phrases describe the circumference of a circle. Practice and Problem Solving d 5 3. r.5 The radius is.5 centimeters. d 8. r The radius is millimeters. 5. 3 d 3 r The radius is 3 inches.. d r ( ) The diameter is inches. 8. d r ( ) 0.8.6 The diameter is.6 feet. 9. C πd 3. 0 3. The circumference is about 3. inches. 0. C π r The circumference is about inches.. C πd 3. 8 56.5 The circumference is about 56.5 inches.. Sample answer: You need to know the circumference of a circular pond to border the pond with decorative stones. The pond has a diameter of feet. C πd 3..56 The circumference is about.56 feet. 3. a. Diameter of sinkhole: C πd 5.36 3. d Round 5.36 down to 5. Round 3. down to 3. 5 3d 5 d The diameter is about 5 meters. Diameter week later: C πd 50. 3. d Round 50. down to 50. Round 3. down to 3. 50 3d 50 d The diameter week later is about 50 meters. b. The diameter of the sinkhole is about 50 times greater than the previous week. 5. a. Circle D has the greatest circumference. Sample answer: The diameter of Circle D is 00 inches, which is 8 feet. Because Circle D has the greatest 3 diameter, the circumference will be the greatest. b. Circle B has the least circumference. Sample answer: The diameter of Circle B is less than feet. Because Circle B has the least diameter, the circumference will be the least. 6. d r ( ) 6 The diameter is centimeters. 0
C π d 3. 3 5.. So, the perimeter is about 3 +..feet. 6. C π r πr 3. 0 6.8 So, the perimeter is about ( 0) + 6.8 0.8 centimeters.. Smaller circle: C π r 3. 5 3. The circumference of the smaller circle is about 3. centimeters. Larger circle: C π r 3. ( 5 + 5) 3. 0 6.8 The circumference of the larger circle is about 6.8 centimeters. 8. Smaller circle: C πd 3. 9 8.6 The circumference of the smaller circle is about 8.6 feet. Larger circle: C πd (.5 + 9 +.5) The circumference of the larger circle is about feet. 9. Smaller circle: C π r 3. 3. 69.08 The circumference of the smaller circle is about 69.08 meters. Larger circle: C π r 3. 38.6 The circumference of the larger circle is about 38.6 meters. 0. circumference πr π r radius r r Yes, the ratio circumference radius π is π for every circle. C πd. Circumference of semicircle: 3. 3 00.8 50. cm So, the wire is about ( 50.) 00.96 centimeters.. The circle has a diameter of π, so use a diameter of about 3. inches. π in. 3. a. C π r 3. 585 36,63. The minimum distance that a pilot must fly is about 36,63. kilometers. b. Answer should include, but is not limited to: Research is used to find a reasonable average rate of speed for a particular class of aircraft. The qualifying distance in part (a) is used to find the minimum time needed to fly the qualifying distance.. a. Circumference of small tire: C π r 3. 9 ft 56.5 in. in. Rotations: 600. Circumference of large tire: C. ft πd 3. 60 ft 88. in. in. 5. ft Rotations: 600 5. 38 The small tire makes about rotations and the large tire makes about 38 rotations. b. Sample answer: Two large wheels, because you wouldn t have to pedal as much to go the same distance as a bicycle with two small wheels.
5. a. Find the length of the minute hand. Length 50% of 36 mm.5 36 5 mm The minute hand makes 3 of a rotation in 5 minutes. Find 3 of the circumference of a circle with a radius of 5 mm. 3 3 3 C ( πr) πr 3. 5 5.3 So, the tip of the minute hand moves about 5.3 millimeters in 5 seconds. b. Find the circumference of the circle traced out by the minute hand. C π r 3. 5 339. The minute hand moves about 339. millimeters in hour. The hour hand moves only the distance around the clock in hour. So, find the circumference of a circle with a radius of 36 millimeters. C ( πr) πr 3. 36 8.8 6 6 The hour hand moves about 8.8 millimeters in hour. So, the tip of the minute hand moves about 339. 8.8 30.8 millimeters farther in hour. Fair Game Review 6. P w ( ) ( ) + + + 8 The perimeter is feet.. P 6 + 9 + 5 0 The perimeter is 0 meters. 8. P 6 + + 5 + 65 The perimeter is 65 inches. 9. D; Ordered data: 5, 9,, 6, 0,, 5, The middle two values are 6 and 0. Median: 6 + 0 36 8 Section 8. 8. Activity (pp. 3 35). a. Perimeters: Figure : + + + Figure : + + + 6 Figure 3: + 3 + + 3 8 Figure : + + + 0 Pattern: The perimeter of each figure is greater than the last. The next 6 perimeters are,, 6, 8, 0, and. So, the perimeter of the tenth figure is. b. Perimeters: Figure : + + + Figure : + + + + + 8 Figure 3: + + + + + + 3 + 3 Figure : + + + + + + + + + 6 Pattern: The perimeter of each figure is greater than the last. The next 6 perimeters are 0,, 8, 3, 36, and 0. So, the perimeter of the tenth figure is 0. c. Perimeters: Figure : π + + 3. + 5. Figure : π + + 3. + 6.8 + 8.8 Figure 3: π 3 + + 3. 3 + 9. +. Figure : π + + 3. +.56 +.56 Pattern: The perimeter of each figure is π greater than the last. The next 6 perimeters are about., 0.8, 3.98,., 30.6, and 33.. So, the perimeter of the tenth figure is about π 0 + 3. 0 + 33... a. Perimeter of rectangular corral: P Perimeter of trapezoidal corral: P s + s + s3 + s 50 + + + 0 68 + w + 0 8 + 0 88 ( ) ( ) Total amount of fencing: 88 + 68 556 So, a rancher needs 556 yards of fencing. b. The rancher will need less fencing. By combining the corrals, you are eliminating the fencing for two 0-yard sides. So, the rancher needs only 556 ( 0) 6 yards of fencing.
c. Sample answer: The corrals can be combined by stacking them. This eliminates the fencing for two -yard sides. So, the rancher needs only 556 08 yards of fencing. 50 yd ( ) 8. On Your Own (pp. 36 3). Length of grid square lengths: units Length of diagonal lengths:.5 8 units So, the perimeter is about + 8 3 units. 0 yd 0 yd yd yd 0 yd. Length of 6 grid square lengths: 6 6 units Length of 5 diagonal lengths: 5.5.5units So, the perimeter is about 6 +.5 33.5 units. 3. Distance around triangular part: + 0 3 C πd Distance around semicircle: 3. a. 33 tiles b. Sample answer: Hourly wage: $5 Cost of tiles: $ 33 $53 Time to install tiles: 33 33 h $5 Total wages: 33 hour $83.5 hour Bid Cost of tiles + Total wages $53 + $83.5 $363.5 Profit Bid Cost of tiles $363.5 $53 $83.5 So, using an hourly wage of $5 per hour, the amount of the bid is $363.5. An estimate of the profit is $83.5.. To find the perimeter of a composite figure, find the distance around the figure. Sample answer: m 8 m m m πd Perimeter + + 8 + 3.( ) + + 8 + 8.0 + + 8 + 3.8 So, the perimeter is about 3.8 meters. So, the perimeter is about 3 + 0.8.8 centimeters.. C πd 3. 8 5. So, the perimeter is about 8 + 8 + 5.. meters. 8. Exercises (pp. 38 39) 3. 6 0.8 Vocabulary and Concept Check. no; The perimeter of the composite figure does not include the measure of the shared side.. Sample answer: Practice and Problem Solving 3. Length of 6 grid square lengths: 6 6 units Length of 9 diagonal lengths: 9.5 3.5 units So, the perimeter is about 6 + 3.5 9.5 units.. Length of 8 grid square lengths: 8 8 units Length of 8 diagonal lengths: 8.5 units So, the perimeter is about 8 + 0units. 5. Length of 6 grid square lengths: 6 6 units Length of diagonal lengths:.5 6 units Length of long slanted lengths: 0.5 3 units Length of short slanted lengths: 0.5 0.5 unit So, the perimeter is about 6 + 6 + 3 + 0.5 5.5 units. 3
6. Length of 8 grid square lengths: 8 8 units So, the perimeter is 8 units.. Length of grid square lengths: units Length of 6 diagonal lengths: 6.5 9 units Length of 6 slanted lengths: 6 6 units So, the perimeter is about + 9 + 6 9 units. 8. Length of grid square lengths: units Length of 0 diagonal lengths: 0.5 5 units Length of nearly square, slanted lengths: 0.5 3 units So, the perimeter is about + 5 + 3 30 units. 9. Perimeter 5 + 5 + + + + 5 + + 5 56 The perimeter is 56 meters. 0. Perimeter 5 + 8 + 3 + 5 + 3 + 8 8 The perimeter is 8 inches.. Perimeter 9.5 + 6.5 + + + 6 30 The perimeter is 30 centimeters.. The length of the rectangle was counted twice. Perimeter + 3 + + 5 + 0in. 3. Distance around parallelogram part: 5 + + 9 C πd Distance around semicircle: 3. 5.85 So, the perimeter is about 9 +.85 6.85 inches.. Distance around trapezoid part: 5 + + 5 C π r Distance around semicircle: πr 3. 9 8.6 So, the perimeter is about + 8.6 50.6 inches. 5. Distance around square parts: 3 + 3 + 3 + 3 + 3 + 3 8 Distance around semicircles: C πd 3. 6 8.8 So, the perimeter is about 8 + 8.8 36.8 feet. 6. Perimeter 0 + 85 + 50 + 50 + 50 85 The perimeter of the pasture is 85 feet. Convert feet to yards using the fact that there are 3 feet in yard. 85 ft yd 65 yd 3ft Cost 65 6,85 It will cost $6,85 to fence in the pasture.. The distance around the straight part is 300 + 300 600 feet. The distance around the circular part is 0% of π r 0.0 3. 5 565. feet. So, the total distance around the field is about 600 + 565. 65. feet. The time it will take the person to run around the field is about 65. 9 9.5 seconds. 8. The starting points are staggered so that each runner can run the same distance and use the same finish line. This is necessary because the circumference is different for each lane. The diagram shows this because the diameter is greater in the outer lanes. 9. Sample answer: By adding the triangle shown by the dashed line to the L-shaped figure, you reduce the perimeter. d Fair Game Review 0. () ().5 3.5 9 9.35. () ( ).3 8.3 6 9.68
. ( ) ( ) 3. 3. 9 53.86 3. () ( ) 8. 5 8. 5 05 5y + y 5y + + y 5y + + y 5y + y + + + 9y 0. D; ( ) ( ) Study Help Available at BigIdeasMath.com. Quiz 8. 8. d 36. r 8 The radius is 8 centimeters.. d r ( ) The diameter is inches. ( 5 ) y ( ) 3. Length of grid square lengths: units Length of diagonal lengths:.5 6units So, the perimeter is about + 6 8 units.. Length of 6 grid square lengths: 6 6 units Length of diagonal lengths:.5 6 units Length of 8 long slanted lengths: 0.95 3.8 units Length of short slanted lengths:. 5.6 units So, the perimeter is about 6 + 6 + 3.8 + 5.6. units. 5. Length of 8 grid square lengths: 8 8 units Length of slanted lengths: 0.5 3 units So, the perimeter is about 8 + 3 units. 0. Distance around triangular part: 8 + 6 Length of straight part: 0 Circumference of semicircle ends: C πd 3. 8 5. So, the perimeter is about + 0 + 5. 9. feet. C π d 3. 3.. So, the perimeter is about 3 +.. feet.. C πd 3. 8 5. The circumference of the button is about 5. millimeters. 3. Perimeter + + 8 + 0 + 6 60 So, 60 feet of fencing is needed to surround the garden.. Circumference of larger pan: C πd 3. 3.68 in. Circumference of smaller pan: C πd in. The circumference of the larger pan is about 3.68 5.68 inches greater than that of the smaller pan. Section 8.3 8.3 Activity (pp. 33 333). a. The 0-by-0 square contains 00 grid squares. So, the area of the 0-by-0 square is 00 square units. b. Region 6. C π r 3. 6 3.68 The circumference is about 3.68 millimeters. Area square unit square unit square unit. C πd 3..5. The circumference is about. feet. 8. C πd The circumference is about centimeters. 9. Perimeter 8 + 0 + + + 6 + 8 88 The perimeter is 88 inches. 5
6 c. Subtract the areas of the orange, red, and green regions from the area of the large 0-by-0 square. Area of orange grid squares: square units Area of red triangle regions: square units Area of 8 green triangle regions: 8 8 square units Area of circle 00 ( + + 8) 00 8 The area of the circle is about 8 square units. d. The area of the large square is 00 square units. You know that 5 5 and 5 00. Area of large square 5 The area of the circle is about 8 square units. You know that 5 5. What number times 5 is 8? Divide 8 by 5 to find the number 8 5 3.. Area of circle 3. 5 e. The 5 represents the radius. The area of the circle is about 3 r.. d. The height of the parallelogram is approximately r, the radius of the circle. Because the sections alternate with half of the circumference on top and half of the circumference on the bottom, the base of the parallelogram is half of the circumference. C ( πr) πr So, the base of the parallelogram is π r. e. Area of parallelogram b h πr r π r The area of the parallelogram is approximately πr. Because the parallelogram was formed from the circle, you can conclude that the area of the circle is approximately π r. 3. Sample answer: You can estimate the area of a circle by using a grid of unit squares, or by dividing the circle into equal sections, then using them to form a parallelogram so you can find its area.. A formula for the area A of a circle with radius r is A πr. Sample answer: A dinner plate has a radius of 5 inches. A πr 3. 5 3. 5 8.5 The area of the dinner plate is about 8.5 square inches. 8.3 On Your Own (pp. 33 335) A πr 3. 6 3. 36 3.0 The area is about 3.0 square feet... The radius is 8 meters. 8 A πr 96 The area is about 66 square meters. 66 3. The diameter of the tire is the distance across the tire through the center. So, the diameter best describes the height.. The radius of the semicircle is 8 meters. π r A 3. 3. 6 5. The area is about 5. square meters. 5. The radius of the semicircle is 5.5 yards. ( ) A π r 3..5 3. 6.5 9.85 The area is about 9.85 square yards. π r A 3. 3. 6. 89.9 The area is about 89.9 square centimeters. 8.3 Exercises (pp. 336 33) Vocabulary and Concept Check. To find the area of a circle given its diameter, first find the radius by dividing the diameter by. Then use the formula A πr to find the area.. The question What is the area of a circle with a radius of 00 cm? is different. The circles in the other three questions would all have diameters of 00 centimeters. Area of circle with radius of 00 cm: A πr 3. 00 3. 0,000 3,00 The area is about 3,00 square centimeters. Area of circle with diameter of 00 cm: A πr 3. 50 3. 500 850 The area is about 850 square centimeters. Practice and Problem Solving 3. A πr 3. 9 3. 8 5.3 The area is about 5.3 square millimeters.. A r 96 π 8 66 The area is about 66 square centimeters.
A πr 3. 0 3. 00 3 The area is about 3 square inches. 5. 6. The radius is 3.5inches. ( ) A πr 3..5 3..5.065 The area is about.065 square inches.. The radius is centimeter. A πr 3. 3. 3. The area is about 3. square centimeters. 8. The radius is.5 0.5 foot. ( ) A πr 3. 0.5 3. 0.565.665 The area is about.665 square feet. 9. The radius is 56 8 millimeters. A πr 3. 8 3. 8 6.6 The area is about 6.6 square millimeters. 0. A πr 3. 5 3. 5 8.5 The area is about 8.5 square feet.. The radius is 6 inches. A πr 3. 6 3. 36 3.0 The area of the tortilla is about 3.0 square inches.. Hillsboro Inlet Lighthouse: A πr 3. 8 3. 8 6.6 Jupiter Inlet Lighthouse: A πr 3. 8 3. 3 0.36 Difference in areas: 6.6 0.36. The Hillsboro Inlet Lighthouse lights up about. more square miles than the Jupiter Inlet Lighthouse. 3. The radius is 0 0 centimeters. A π r 3. 0 3. 00 The area is about 68 square centimeters. 68 5. The radius is foot. 6. a. π r A 3. 3..5 The area is about.5 square feet. C πr A π r ( ) ( ) r : π π π π ( ) ( ) r : π π 8π 6π () () ( π) π r 8: π 8 π 8 6 6 ( ) ( ) r 6: π 6 π 6 3π 56π Radius Circumference Area π in. π in. 8π in. 8 6π in. 6 3π in. b. When you double the radius of a circle, the circumference doubles. When you double the radius of a circle, the area becomes four times as great. c. Find the circumference and area of a circle with a radius of 3 inches, 9 inches, and inches. C πr A π r () () r 3: π 3 π 3 6π 9π ( ) ( ) r 9: π 9 π 9 8π 8π ( ) ( ) r : π π 5π 9π π in. π in. 6π in. 6π in. 56π in. When you triple the radius of a circle, the circumference triples. When you triple the radius of a circle, the area becomes 9 times as great.. The radius is inches. π r A 3. 3. The area is about 6.08 square inches. 6.08. The running area is 3 of a circle with a 0-foot radius. 3 3 3 3 A πr 3. 0 3. 00 9 The dog has a running area of about 9 square feet.
8. The circle s diameter is one-half as long, so it equals the radius of the semicircle. A diagram shows that the area of the semicircle is greater than the area of the circle. x Area of shaded region area of square areas of unshaded regions ( ) 0.86 + 0.86.8 x ft 9. The shaded region is identical to the unshaded region, so find half the area of the circle. The radius is 5.5 inches. ( ) A π r 3..5 3. 6.5 9.85 The area is about 9.85 square inches. 0. The four corner sections can be rearranged to form a circle. So, the area of the shaded region is equal to the area of the square minus the area of the circle with a diameter of 9 meters. Area of square: A s 9 8 The circle s radius is 9.5 meters. Area of corner sections: A π r 3. (.5) 3. 0.5 63.585. Area of shaded region: 8 63.585.5 So, the area is about.5 square meters. ft ft Draw a -foot square about the smaller shaded region. Subtract the area of a quarter-circle with a -foot radius from the area of the square to find the area of each unshaded region. Area of an unshaded region area of square area of circle s πr ( 3.)( ) 3. 0.86 Subtract the areas of both unshaded regions from the area of the square to find the shaded area. Subtract the area of the smaller shaded region from the area of a semicircle with a -foot radius to find the area of one unshaded region of the whole figure. Area of unshaded region Area of semicircle Area of small shaded region πr.8 ( 3. )( ).8 6.8.8 Subtract the total areas of the unshaded regions from the area of a quarter-circle with a -foot radius to find the total area of the shaded regions. Area of shaded region Area of circle Areas of unshaded regions πr ( + ) ( 3. )( ) 8.56 8.56 The area of the shaded regions is.56 square feet. Fair Game Review + 6 5 8 + 30 + 30. ( )( ) ( ) ( ) 8 + 3 6 + 3 3 + 53 3. ( ) ( ) 6 + 6 + + 3. ( ) ( ) 5. A; ft 5 5 8 3 3 5 3 5 3 5 5 85 8 3 3 8
Section 8. 8. Activity (pp. 338 339). Answer should include, but is not limited to: a. An enlarged outline of a state on grid paper. b. Area is estimated by counting unit squares. c. Sample answer: The easiest to find have rectangular outlines. The areas of states with curved outlines are difficult to find because the curves do not follow the grid lines.. Answer should include, but is not limited to: a. Reasonable estimates for the areas of all six pieces. b. Estimates are added to see if the total is close to 50 square centimeters. It is explained why this can be used as a check. 3. None of the patterns fill more, because they all have the same area. In each pattern, the area of the circles is the number of circles times π r. So, you have: π 6π a. ( ) π 6π b. ( ) c. 6 π() 6π 3. Area of rectangle: A w ( ) 9 63 A bh 9 6 Area of triangle: ( )( ) So, the area is 63 + 90 square meters.. Area of square: A Area of semicircle: s π r 3. A.5 Area of semicircles:.5 6.8 So, the area is about + 6.8 0.8 square feet. 8. Exercises (pp. 3 33) Vocabulary and Concept Check. Sample answer: () Add the areas of a rectangle and triangle. The rectangle has length 8 inches and width inches. The triangle has base 6 inches and height 6 inches. () Add the areas of a rectangle and trapezoid. The rectangle has length inches and width inches. The trapezoid has base lengths of inches and 0 inches, and a height of 6 inches.. Sample answer: Divide the trapezoid into two triangles and a rectangle. d. 6 π 6π. Sample answer: You can find the area of a composite figure by finding the areas of all the pieces that make up the figure, and then finding the sum of those areas. 5. Answer should include, but is not limited to: A list of area formulas for squares, rectangles, triangles, trapezoids, parallelograms, and circles. A sample composite figure made up of each type of basic figure with dimensions labeled and area calculated. 8. On Your Own (pp. 30 3). Area of 33 squares: 33 33 square units Area of half squares: 0.5 square unit Area of 3 three-quarter squares: 3 0.5.5 square units Area of 3 one-quarter squares: 3 0.5 0.5 square unit So, the area is 33 + +.5 + 0.5 3 square units.. Area of 6 squares: 6 6 square units Area of 0 half squares: 0 0.5 5 square units So, the area is 6 + 5 5 square units. Practice and Problem Solving 3. Area of squares: square units Area of 3 half squares: 3 0.5.5 square units So, the area is +.5 8.5 square units.. Area of 30 squares: 30 30 square units Area of 6 half squares: 6 0.5 3 square units So, the area is 30 + 3 33 square units. 5. Area of 0 squares: 0 0 square units Area of 0 half squares: 0 0.5 5 square units So, the area is 0 + 5 5 square units. 6. Area of squares: square units Area of 6 half squares: 6 0.5 3 square units So, the area is + 3 30 square units.. Area of 0 squares: 0 0 square units Area of 0 half squares: 0 0.5 5 square units So, the area is 0 + 5 5 square units. 9
8. Area of 0 squares: 0 0 square units Area of 8 half squares: 8 0.5 square units So, the area is 0 + square units. 8 A b + B h ( + 9 )( 8 ) ( 6 )( 8 ) 0 9. Area of rectangle: A w ( ) Area of trapezoid: ( ) So, the area is 8 + 0 3 square centimeters. 5 60 0. Area of rectangle: A w ( ) Area of semicircles: A πr 3..5 3. 56.5 6.65 ( ) ( ) So, the area is about 60 + 6.65 36.65 square feet.. Answer should include, but is not limited to: Tracings of a hand and foot on grid paper, estimates of the areas, and a statement of which is greater.. Area of rectangle: A w 3() 8 0 Area of triangle: A bh ( 5 )( 6 ) 5 So, the area is 0 5 89 square meters. 3. To find the area, draw a rectangle on the figure as shown. 5 in. in. in. 5 in. Find the area of the large triangle, then subtract the area of the rectangle. Area of large triangle: A bh ( )( 9 ) 3.5 A w 8 Area of rectangle: ( ) So, the area is 3.5 8 3.5 square inches.. Area of square: A s 6 36 Area of semicircle: A πr 3. 3 3. 9.3 So, the area is about 36.3.8 square feet. 5. Area of left triangle: A bh ()() 3 0.5 9 3 3.5 Area of right triangle: A bh ( )( ) So, the area of the shaded region is 0.5 3.5 + square meters. 6. Circumference of semicircles: πd C πd 3.( 0) 6.8 Circumference of quarter circle: C ( π r) ( 3. 0) 3. So, the perimeter of the fountain is about 6.8 + 3. 9. feet. Area of semicircles: A πr 3. 0 3. 00 3 Area of quarter circle: A πr 3. 0 3. 00 3 So, the area of the fountain is about 3 3 68 + square feet. 50
. a. Left envelope Area of rectangle: A w ( ) 5.5.5.5 Area of triangle with height 3 inches and base.5 inches: A bh (.5 )( 3 ) 6.5 Area of triangle with height.5 inches and base 5.5 inches: A bh ( 5.5 )(.5 ) 6.85 So, the total area of the left envelope is.5 + 6.5 + 6.85 5 square inches. Right envelope ( ) ( ) Area of large rectangle: A w ( ) 0 5.5 55 A b + B h ( +.5 )( 0.5 ) ( 8.5 )( 0.5 ) 3.85 Area of trapezoid flap: ( ) So, the total area of the right envelope is 55 + 3.85 6.35 square inches. ( ) Because 6.35 is greater than 5, the right envelope has the greater area. b. 500 envelopes use 500( 6.35) 30,68.5 square inches of paper for the design on the right. Divide this amount by the amount of paper the design on the left uses. 30,68.5 5 590 So, the design on the left can make 590 500 90 more envelopes. Fair Game Review 8. x 9. y 6 0. b + 3. w. A; 0.0% of 50 0.000 50 0.0 Quiz 8.3 8.. Area of squares: square units Area of half squares: 0.5 square units So, the area is + 6 square units.. Area of squares: square units Area of 8 half squares: 8 0.5 square units So, the area is + 8 square units. A πr 3. 3. 5.6 The area is about 5.6 square inches.. 5. The radius is 6 3 centimeters. A πr 3. 3 3. 9 8.6 The area is about 8.6 square centimeters. 6. radius: 3 A πr 9 6 9 6 8 5 9 8 The area is about 8 5 9, or 9.65, square inches. 8. Area of square: A s Area of triangle: A bh ( )( 9 ) 5 So, the area is + 5 98 square feet. 8. Area of semicircle: A πr 3. 3. 6.8 A b B h ( + 6 )( ) ( 0 )( ) 0 Area of trapezoid: ( + ) So, the area is about 6.8 + 0 6.8 square meters. 3. Area of squares: square units Area of half squares: 0.5 square units So, the area is + 9 square units. 5
9. Area of rectangle: A w ( ) Area of parallelogram: A bh ( ) 50 5 50 0 0 600 Area of square: A s 0 00 So, the area is 50 + 600 + 00 50 square centimeters. A πr 3. 3.5 3..5 38.65 0. ( ) The area of the pot holder is about 38.65 square inches.. Area of square: A s 8 6 Area of semicircles: A πr 3. 3. 6 50. So, the area of the card is about 6 + 50.. square centimeters.. The radius is 8 inches. 96 A πr 308 The area of the desktop is about 308 square inches. 3. Area of floor: A s 96 9 Area of rug: A πr 8 5 So, there is about 96 5 square feet for floor space not covered by the rug. Chapter 8 Review d 8. r The radius is inches. d 60. r 30 The radius is 30 millimeters. d 00 3. r 50 The radius is 50 meters. d 3. r.5 The radius is.5 yards. 6. d r ( ) 5 0 The diameter is 0 meters.. d r () The diameter is inches. 8. d r ( ) 5 50 The diameter is 50 millimeters. 9. C π r 3. 3 8.8 The circumference is about 8.8 feet. 0.. C πd 3 66 The circumference is about 66 centimeters. C πd 6 3 The circumference is about 3 inches.. Perimeter + 5 + + 5 + 9 The perimeter is inches. 3. Perimeter 9 + 9 + 9 + + 9 + 30 + 9 96 The perimeter is 96 feet.. Perimeter 3 + 5 + 0 + + 0 6 The perimeter is 6 centimeters. 5. Distance around triangular part: 0 + 0 0 C π r Distance around semicircle: πr 3. 6 50. So, the perimeter is about 0 + 50. 90. millimeters. 6. Distance around square part: 6 + + + 6 + + 6 Distance around semicircles: C πd 3..56 So, the perimeter is about 6 +.56 8.56 inches. 5. d r ( ) 0 0 The diameter is 0 feet. 5
. Distance around trapezoidal part: 0 + 6 + 8 C πd Distance around semicircle: 3. 8.8 So, the perimeter of the figure is about 8.8.8 + centimeters. 8. A πr 3. 3. 6 50. The area is about 50. square inches. 9. A πr 3. 3. 39.9 The area is about 39.9 square centimeters. 0. The radius is millimeters. A π r 63 386 The area is about 386 square millimeters.. Area of rectangle: A w ( ) Area of semicircle: 0 0 A πr 3. 5 3. 5 39.5 So, the area is about 0 + 39.5 9.5 square inches.. Area of square: A s Area of parallelogram: A bh 53 () 5 Area of rectangle: A w ( ) 5 0 So, the area is + 5 + 0 9 square inches. 6 Area of semicircles: A πr 3. (.5) 3. 6.5 9.65 3. Area of triangle: A bh ( )( ) So, the area is about + 9.65 3.65 square feet. Chapter 8 Test d 0. r 5 The radius is 5 inches. d 5. r.5 The radius is.5 yards. 3. d r ( ) 3 68 The diameter is 68 feet.. d r ( ) 9 38 The diameter is 38 meters. 5. C πd 3..56 The circumference is about.56 feet. The radius is feet. A πr 3. 3..56 The area is about.56 square feet. 6. C π r 3. 6.8 The circumference is about 6.8 meters. A πr 3. 3. The area is about 3. square meters.. C πd 0 0 0 The circumference is about 0 inches. The radius is 0 35 inches. 5 A πr 35 5 3850 The area is about 3850 square inches. 8. Length of grid square lengths: units Length of diagonal lengths:.5 3 units So, the perimeter is about + 3 5 units. Area of 8 squares: 8 8 square units Area of half squares: 0.5 square unit So, the area is 8 + 9 square units. 53
9. Perimeter 5 + 5 + + 8 + 6 The perimeter is 6 meters. Area of triangle: A bh ()() 8 3 A w 8 3 Area of rectangle: ( ) So, the area is + 3 square meters. 0. Perimeter 0 + 6 + + 0 + 8 + 8 The perimeter is 8 inches. Area of triangle: A bh ( 6 )( 8 ) Area of rectangle: A bh 66 ( ) 36 Area of triangle: A bh ()() 8 6 So, the area is + 36 + 6 96 square inches.. Distance around rectangular part: + + 8 C πd Distance around semicircle: So, the perimeter is about + 3( ) 08 meters. Area of rectangle: A w 8( ) 39 Area of semicircle: A πr ( ) 9 5 So, the area is about 39 + 3( ) 63 square meters.. Perimeter 0 + 60 + 0 + 0 + 0 + 0 00 The museum needs 00 feet of rope. 3. C πd 3..9 9.06 You will need about 9.06 meters of chicken wire.. Let R be the radius of the entire symbol. Then the circumference of the symbol is π R and the circumference of the large semicircle of the yin is π R π R. In the two semicircles separating the yin and yang, each diameter is R. Circumference of two small semicircles: C πd πr π R So, the perimeter of the yin symbol is πr + πr πr. The circumference of the entire yin and yang symbol is equal to the perimeter of the yin. Chapter 8 Standards Assessment. C; Convert quarts to 8 cups. soup servings soup servings cups cups 6 x 5 8. ; The angles are vertical angles. Because vertical angles are congruent, the angles have the same measure. x + 85 x 8 x So, the value of x is. 3. I; n 5. C; r d 8 The radius of the circle is centimeters. A πr 5 6 55 The area is about 55 square centimeters. 5. H; Finding the area of the vertical rectangle and the area of the horizontal rectangle means that the area the two rectangles share in common ( the 3 3 center square) has been counted twice. 6. B; 5x 3 5x x.8 The solution is x.8. 5
. 9.; Distance around semicircle: C πd 3.( 6) 9. Distance around straight sides: + 6 + 0 So, the perimeter is about 9. + 0 9. units. 8. G; 3x 8 3x x Because 5, 5 is in the solution set. 9. A; Store A: 0% of 5 0.0 5 5 So, the sale price is 5 5 $60. Store B: 35% of 00 0.35 00 35 So, the sale price is 00 35 $65. Store C: 0% of 0 0.0 0 So, the sale price is 0 $63. Store D: 30% of 95 0.30 95 8.50 So, the sale price is 95 8.50 $66.50. Store A has the least price for the earrings. 0. Part A: Area sprayed 3 area of circular region 3 πr 3 ( 3. )( 0 ) 3 ( 3. )( 00 ) 9 The sprinkler sprays 9 square feet. Part B: 3 circumference circumference of circle + radius + radius 3 ( πr) + r 3 ( )( 3. )( 0 ) + ( 0 ) 9. + 0 3. 0 0 The sprinkler sprays a region with a perimeter of 3. feet. 55