Math-2A. Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms

Transcription

1 Math-A Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms

2 Describe the idea of area. Area attempts to answer the question how big is it? The area of this square is.? 1 inch 1 inch area = length * width area = (1 inch)(1 inch) area 1inch area = 1 square inch When we ask for an area, we really mean, how many 1 inch x 1 inch squares will fit in the area.

3 1 inch The area of this circle is.? how many 1inch squares will fit in the circle. 1 inch area less than 4 inch Will all those extra corners make up 1 sq. inch? No. They make up slightly less than 1 sq. inch. area slightly more than 3inch area inch

4 What is the definition of pi? distance around the circle distance across the circle Circumference diameter C D C D Circumference radii C r C r

5 The area of this circle is.? area r What is the area of the circle given by the equation? 16 x ( y area 16 )

6 .7 inch The area of this circle is.? A r Is the given dimension a radius? area in If decimal dimensions are given in the problem, it is OK to have a decimal answer. If the problem says to use 3.14 for pi, DO NOT use the pi button on your calculator; use 3.14.

7 The area of this triangle is.? 4 in A 1 *base*height 3 in Base (of a triangle): any side of the triangle. height (of a triangle): the perpendicular distance (altitude) from any vertex of the triangle to its opposite side. height (of a triangle) is the same at its altitude.

8 The altitude of a triangle. A 1 *base*height Area formula: requires the use of matching altitudes and sides.

9 Area ΔABC =? Area 0.5*base*height C Drop an altitude to the longest side. a=14 h b=3 sin 33.6 = h 3 h º B c=5 33.6º A 3 (sin 33.6) = h h = 1.7 Area ΔABC = (1.7) Area ΔABC = units

10 The width of a rectangle is feet. The length is twice the width. What is the perimeter of the rectangle? W L L W w = L = w substitution L = = 4 P L w substitution rectangle P rect. = 4 + () P rect. = 1 ft

11 The width of a rectangle is 3 feet. The length is four times the width. What is the area of the rectangle? w = 3 L = 4w substitution L = 4 3 = 1 Area l * w substitution rectangle A rect. = (1 ft)(3 ft) A rect. = 36 ft W L L W

12 If the width of a rectangle is twice the length, and the perimeter is 90 feet, what is the area? w = L P substitution rect. = 90 ft P L w rectangle W L L W 90 = L + (L) solve for L 90 = 6L L = 15 w = 30 substitution w = L substitution A = L w A rect. = (15 ft)(30 ft) A rect. = 450 ft

13 The area of a trapezoid is the average of the two bases times the height. 1 A b1 b h One base has a length of 6 feet. The other base is three times as long. If the area of the trapezoid is 75 square feet, what is the height? b 1 = 6 ft substitution b = 3 6 ft = 18 ft b = 3b 1 A = 75 ft substitution A = 0.5 b 1 + b h 75 = h 75 = 1h solve for h h = 6.5 ft b 1 b h

14 What does surface area mean? Surface area: The area of the surface of the shape. Why would this information be important? Helps you to know how much material you need to build, paint, or cover the item.

15 A Solid : a three-dimensional shape. Prism: a solid that has two parallel polygonal bases and planer ( flat ) sides. Prisms are named based upon the shape of their bases. If the sides intersect the base at a right angle, we include that in the name: Right Rectangular Prism Lateral Area: the total area of the sides.

16 Build a net (flatten out the box ). Symbolically we could say: Surface area prism + +

17 What is the surface area of the prism? 4 in 6 in 6 in 4 in 6 in 10 in 10 in 6 in Surface + + area prism 6 in SA = (4 6)

18 Area of a Rectangle The length of a rectangle is 4 more than 3 times its width. The area of the rectangle is 00 square inches. What is the length and width of the rectangle? Area = L * W L = 3W + 4 A = 00 Using substitution: 00 = (3W + 4) * W Solve by graphing. width length

19 Area of a Rectangle Area = L * W L = 3W + 4 A = 00 Using substitution: 00 = (3W + 4) * W y x( 3x 4) 00 Find the zero of the equation. Solve by graphing. Get into zero equals form 0 = W(3W + 4) 00 Let x = width 0 x(3x 4) 00 x = width = 7.53 inches

20 Area of a Rectangle Area = L * W L = 3W + 4 y A = 00 Using substitution: 00 = (3W + 4) * W x( 3x 4) 00 Find the zero of the equation. Using substitution: L = 3W + 4 L = 3(7.53) + 4 L = 6.59 inches Check: 00 = L*W Check: 00 = (6.59)(7.53) x = width = 7.53 inches