This pdf includes the following topics:- Definition and Strategy Examples Applications
1. Notes: Area of Composite Figures
2. I. Definition and Strategy A composite figure is made up of simple shapes, such as triangles, rectangles, trapezoids, and circles. To find the area of a composite figure, find the areas of the simple shapes and then add them together.
3. II. Examples Ex 1a: Find the shaded area. Round to the nearest tenth, if necessary. Divide the figure into parts. area of half circle: area of triangle: area of the rectangle: A = bh = 20(14) = 280 mm2 shaded area: 50 + 280 + 84 ≈ 521.1 mm2
4. Ex 1b: Find the shaded area. Round to the nearest tenth, if necessary. Divide the figure into parts. area of parallelogram: A = bh = 8(5)= 40ft2 area of triangle: shaded area: 40 + 25 = 65 ft2
5. Ex 1c: Find the shaded area. Round to the nearest tenth, if necessary. Area of rectangle: A = bh = 37.5(22.5) = 843.75 m2 Area of triangle: Total shaded area is about 1781.3 m2. = 937.5 m2
6. III. Examples with Subtraction Sometimes you might need to subtract a figure. Ex 2a: Find the shaded area. Round to the nearest tenth, if necessary. area of a triangle: area of the half circle: Subtract the area of the area of figure: half circle from the area 234 – 10.125 ≈ 202.2 ft2 of the triangle.
7. Ex 2b: Find the shaded area. Round to the nearest tenth, if necessary. area of circle: A = r2 = (10)2 = 100 cm2 area of trapezoid: area of figure: 100 –128 186.2 cm2
8. Ex 2c: Find the shaded area. Round to the nearest tenth, if necessary. area of circle: A = r2 = (3)2 28.3 in2 area of square: A = bh (4.24)(4.24) 18 in2 area of figure: 28.3 – 18 = 10.3 in2
9. IV. Applications Ex 3a: A company receives an order for 65 pieces of fabric in the given shape. Each piece is to be dyed red. To dye 6 in2 of fabric, 2 oz of dye is needed. How much dye is needed for the entire order? To find the area of the shape in square inches, divide the shape into parts. The two half circles have the same area as one circle. The area of the circle is (1.5)2 = 2.25 in2. The area of the square is (3)2 = 9 in2. The total area of the shape is 2.25 + 9 ≈ 16.1 in2. The total area of the 65 pieces is 65(16.1) ≈ 1044.5 in2. The company will need 1044.5 ≈ 348 oz of dye for the entire order.
10. Ex 3b: The lawn that Katie is replacing requires 79 gallons of water per square foot per year. She wants to replace the lawn with a xeriscape garden, which only uses 17 gallons of water per square foot per year. How much water will Katie save, per year, by planting a xeriscape garden? Find the area of the figure. Area of large rectangle = bh = 7.5(28.5) = 213.75 ft2 (𝑏1 +𝑏2 )ℎ 12+18 6 Area of trapezoid= = =90 ft2 2 2 Area of small rectangle = bh = 6(12)= 72 ft2 Area of garden = 213.75+90+72=375.75 ft2 Area times gallons of water 375.75(79) = 29,684.25 Subtract water used 29,684.25 – 6,387.75 = 23,296.5 gallons saved.