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1 Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior angles of a quadrilateral is: A. 180 B. 108 C. 360 D The area of the parallelogram is: A. 40 B. 36 C. 96 D The area of the trapezoid is: A. 24 B. 128 C. 64 D. 48

2 6. Find x: x A. 4 B. 2 2 C. 2 3 D Find the area of a circle that has a radius of 4 inches. A. 8π B. 16π C. 12π D. 4π 8. Find the number of degrees of x. 2 3 x A B C D The circumference of a circle with a diameter of 3 cm is: A. 6π B. 9π C. 3π D. 12π 10. The lateral area is: A. 60 B. 120 C. 126 D. 60

3 11. Find x: x 8 4 A B. 4 3 C. 4 2 D Find the volume of this regular pyramid: A B. 384 C. 480 D Find the surface area of the sphere: 5 A. 25 π B. 100 π C π D. 50 π 14. BOC = O B 100 C A. 50 B. 25 C. 100 D. 200

4 15. BAC = A B 43 C A. 43 B. 86 C D The length of chord CD is 12, and its distance from O is 8. Find the radius of the circle. O C D A. 10 B. 12 C. 14 D Find the lateral area of the cone: A. 6 π B. 12 π C. 15π D. 20π

5 18. Find the volume of the cone: A. 36 π B. 9 π C. 15π D. 12π 19. Find the volume of the sphere: 2 A. 24 π B. 8 π C π D. 4 π 20. ABC ~ DEF Find x. A F 5 E B x C D A. 5 4 B. 7 8 C. 1 D. 2

6 21. Find the area of the triangle: A. 48 B. 24 C. 30 D The area of a circle is 80 square feet. Find the approximate radius of the circle. A. 3 B. 4 C. 5 D The area of a square is 16 square cm. What is the perimeter of the square? A. 4 B. 12 C. 16 D Find x: 7 22 x A. 2.6 B. 25 C D Find x: x 22 7 A. 7.5 B. 6.5 C. 2.8 D. 2.6

7 26. Find x: 3 x 7 A. 30 B. 40 C D Which of the following statements is false? A. A parallelogram is a quadrilateral. B. A rectangle is a square. C. A rectangle is a parallelogram. 28. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is always: A. a rhombus B. a rectangle C. a parallelogram. 29. The opposite angles of a parallelogram are always: A. equal B. supplementary C. complementary 30. The diagonals of a rectangle are always: A. equal to each other B. equal and perpendicular to each other C. perpendicular and bisect each other

8 Part II - Problems: 1. Find the shaded area (you may use decimals). shaded area = 2. Solve for x in rhombus BREA, with K = 20x 10 and RE = 8x B R K A E perimeter = 3. Solve for x in rectangle OCEA, with ONC = 2 3 x 6. O C N A 25 E x =

9 4. Find the perimeter of square OVER O V 3 R E perimeter = 5. Find the measure of the variable in each circle Q x = y = z = a = b = c =

10 6. Find the area of a rhombus whose perimeter is 52, and one diagonal is 24. area = 7. Solve for x in the isosceles trapezoid. x 2 2x 8x 24 x = or 8. In isosceles trapezoid CLUB, CU = 3x + 5y and BL = 18. Solve for x and y. L 2x y C B 12 U x = y = 9. The height of a cylinder is 20 ft. The volume of that cylinder is 500π ft 3. Find the radius of the cylinder. radius = (include units)

11 10. Find the volume of a cube whose diagonal is 6 inches. perimeter = (include units) 11. Find the exact area of the shaded region, including units, if the diameter is 16 inches. S R T U V shaded area: 12. Find the exact area (no decimals) of an equilateral triangle whose radius is 8 inches. 8 area = (include units)

12 13. Given the rectangle, find x and y: 3x+2y 2x+6y 6 9 x = y = 14. Given the parallelogram, find x: x 2 - x 20 x = or x = 15. Find the area: area = 16. Solve for x: AD = 3, DB = 6, DE = x 2, BC = x + 4, DE BC. B D A E C x =

13 17. The area of the trapezoid is 46 square inches. Find x, including units. 6 inches x 7 inches x = 18. From a point 12 feet from the foot of a flagpole, the angle of elevation to the top of the pole measures 28. Find the height of the flagpole, including units. Draw and label a picture. height = 19. Find the surface area and volume of the cylinder, including units! 8 cm 6 cm surface area: volume:

14 20. Find the exact area and perimeter of the shaded sector, including units in area = (include units) perimeter = (include units) 21. Mark in the pictures below the 5 ways that you can prove that a quadrilateral is a parallelogram: 22. Find the value of x: a) b) 23.

15 24. D B A Find: BC = AB = 60 4 BD = DC = AD = C 25.

16 26. Fill in all the missing lengths until you can tell what w is. 27. Find the perimeter of the trapezoid, as well as the area Find the area of each shaded segment. area = area =

17 29. Find the area of each: Fill in all other angles and measures of arcs:

18 31. Find the length of each arc of a circle with a radius of 14. (a) a 40 arc (b) a 30 arc (c) a 45 arc 32. Solve each equation for x: a. 3x + 1 ( ) (4x 12) = 0 b. 3 x 1 = 1 x c. x(x 3) = 4 d. x 4 4 = 10 x Find the area of an isosceles triangle whose base is 4 cm long and whose legs are 6 cm long.

19 34. Decide whether each statement is always, sometimes or never true. a. A parallelogram is a square. b. A square is a parallelogram. c. Opposite angles of a parallelogram are supplementary. d. Opposite angles of a trapezoid are congruent. e. The diagonals of a rectangle are congruent. f. The diagonals of a rectangle bisect one another. g. The diagonals of a rectangle bisect the angles of the rectangle. h. Any two consecutive angles in a rhombus are supplementary. 35. A ladder leaning against a building is 25 feet long and it makes an angle of 65 with the ground. How far off the ground is the top of the ladder? Make a sketch first. 36. Find the total surface area of a right rectangular prism whose dimensions are 6 ft by 4 ft by 7 ft. Make a sketch first. 37. AB = 10 in, the radius of the circle is 13 inches. How far is the chord from the center of the circle? A B

20 38. Find the volume and the total surface area of each solid: 12 cm 5 6 The base of the figure is a regular hexagon with each side 6 cm long, the height of the prism is 10 cm, the height of the pyramid is 5 cm.

21 1. Right Prism B = the area of one base L.A. = sum of the areas of the lateral faces T.A. = L.A. + 2B h V = Bh h 2. Right Circular Cylinder L.A. = 2 πrh r h T.A. = L.A. + 2B = 2 πrh + 2 πr 2 V = Bh = πr 2 h 3. Regular Pyramid L.A. = sum of the areas of the lateral faces T.A. = L.A. + B h l V = 1 3 Bh 4. Right Circular Cone L.A. = πr l h r l T.A. = L.A. + B = πr l + πr 2 V = 1 3 Bh = 1 3 πr2 h 5. Sphere r A = 4πr 2 V = 4 3 πr3 REMEMBER: = 5

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