Warm Up Find the area of the following figures. 1. A triangle with a base of 12.4 m and a height of 5 m 2. A parallelogram with a base of 36 in. and a height of 15 in. 3. A square with side lengths of 2.05 yd 31 m2 540 in2 4.2025 yd2

Learn to find the area of irregular figures.

Vocabulary composite figure

A composite figure is made up of simple geometric shapes, such as triangles and rectangles. You can find the area of an irregular figure by separating it into non- overlapping familiar figures. The sum of the areas of these figures is the area of the irregular figure. You can also estimate the area of an irregular figure by using graph paper.

Additional Example 1: Estimating the Area of an Irregular Figure Estimate the area of the figure. Each square represents one square yard. Count the number of filled or almost-filled squares: 45 squares. Count the number of squares that are about half-full: 10 squares. Add the number of filled squares plus ½ the number of half-filled squares: 45 + ( • 10) = 45 + 5 =50 1 2 The area of the figure is about 50 yd2.

Count the number of filled or almost-filled squares: 11 red squares. Check It Out: Example 1 Estimate the area of the figure. Each square represents one square yard. Count the number of filled or almost-filled squares: 11 red squares. Count the number of squares that are about half-full: 8 green squares. Add the number of filled squares plus ½ the number of half-filled squares: 11 + ( • 8) = 11 + 4 =15. 1 2 The area of the figure is about 15 yd . 2

Additional Example 2: Finding the Area of an Irregular Figure Find the area of the irregular figure. Use 3.14 for . Step 1: Separate the figure into smaller, familiar figures. 16 m Step 2: Find the area of each smaller figure. 9 m Area of the parallelogram: 16 m A = bh Use the formula for the area of a parallelogram. A = 16 • 9 Substitute 16 for b. Substitute 9 for h. A = 144

Additional Example 2 Continued Find the area of the irregular figure. Use 3.14 for . 16 m Area of the semicircle: 9 m The area of a semicircle is the area of a circle. 1 2 A = (r)‏ 1 2 __ 16 m A ≈ (3.14 • 82)‏ 1 2 __ Substitute 3.14 for  and 8 for r. A ≈ (200.96) 1 2 __ A ≈ 100.48 Multiply.

Additional Example 2 Continued Find the area of the irregular figure. Use 3.14 for . Step 3: Add the area to find the total area. 16 m 9 m A ≈ 144 + 100.48 = 244.48 16 m The area of the figure is about 244.48 m2.

Find the area of the irregular figure. Use 3.14 for . Check It Out: Example 2 Find the area of the irregular figure. Use 3.14 for . Step 1: Separate the figure into smaller, familiar figures. 8 yd Step 2: Find the area of each smaller figure. 9 yd 9 yd Area of the rectangle: A = lw Use the formula for the area of a rectangle. 3 yd A = 8 • 9 Substitute 8 for l. Substitute 9 for w. A = 72

Check It Out: Example 2 Continued Find the area of the irregular figure. Use 3.14 for . Area of the triangle: 8 yd 9 yd The area of a triangle is the b • h. 1 2 A = bh 1 2 __ 9 yd A = (2 • 9)‏ 1 2 __ Substitute 2 for b and 9 for h. 2 yd A = (18) 1 2 __ A = 9 Multiply.

Check It Out: Example 2 Continued Find the area of the irregular figure. Use 3.14 for . Step 3: Add the area to find the total area. A = 72 + 9 = 81 The area of the figure is about 81 yd2.

Check It Out: Example 3 The Franklins want to wallpaper the wall of their daughters loft. How much wallpaper will they need? 6 ft 23 ft 18 ft 5 ft

Check It Out: Example 3 Continued Solve 3 Find the area of each smaller figure. Area of the rectangle: Area of the triangle: A = lw A = bh 1 2 __ A = 18 • 6 A = (5 • 11)‏ 1 2 __ A = 108 A = (55)‏ 1 2 __ Add the areas to find the total area. A = 27.5 A = 108 + 27.5 = 135.5 The Franklins need 135.5 ft2 of wallpaper.

Lesson Quiz Find the perimeter and area of each figure. 1. 2. 31.42 cm, 62.13 cm2 39.1 ft, 84 ft2