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Areas of Composite Figures and Irregular Shapes Chapter 9 – Lesson 3 Areas of Composite Figures and Irregular Shapes

Objectives Use the Area Addition Postulate to find the areas of composite figures. Use composite figures to estimate the areas of irregular shapes.

Vocabulary composite figure

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 use the Area Addition Postulate.

How could we calculate the area of an irregular figure?

Example 1: Finding the Areas of Composite Figures by Adding Find the shaded area. Round to the nearest tenth.   Area of the trapezoid:   Area of the semicircle: Shaded area: 364 + 50 ≈ 521.1 mm2

Check It Out! Example 1a Find the shaded area. Area of the parallelogram: A = bh = 8(5) = 40 ft2   Area of the triangle: Shaded area: 40 + 25 = 65 ft2

Check It Out! Example 1b Find the shaded area. Round to the nearest tenth.   Area of the triangle:   Area of the semicircle: 234 – 10.125 ≈ 202.2 ft2 Shaded area:

Check It Out! Example 1c Find the shaded area. Round to the nearest tenth. Area of the circle:     Area of the trapezoid: Shaded area: 100 – 128 ≈ 186.2 cm2

Example 2 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? Area of the circle:   Area of the square:   Shaded area: 2.25 + 9 ≈ 16.1 in2 Area of the 65 pieces: 65(16.1) ≈ 1044.5 in2 scale factor: 3 to 1  

Example 3 To estimate the area of an irregular shape, you can sometimes use a composite figure. First, draw a composite figure that resembles the irregular shape. Area of rectangle: A = lw = (3)(2) = 6 ft2 Area of half circle: Area of isosceles triangle:   Area of right triangle: The shaded area is about 12 ft2.

Check It Out! Example 3 Use a composite figure to estimate the shaded area. The grid has squares with side lengths of 1 ft. Area of the square:   Area of triangle:   3 triangles: 3 ft2   Area of the trapezoid: The shaded area is about 9 ft2.

Lesson Summary: Objectives Use the Area Addition Postulate to find the areas of composite figures. Use composite figures to estimate the areas of irregular shapes.

Preview of the Next Lesson: Objectives Find the perimeters and areas of figures in a coordinate plane.

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