9-6 Area of Irregular Figures Course 2 Math Minute Math Minute Lesson Presentation Lesson Presentation Vocabulary

Math Minute 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. yd 31 m in 2 Course Area of Irregular Figures 4 yd 2

Learn to find the area of irregular figures. Course Area of Irregular Figures

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. Course Area of Irregular Figures

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) = = The area of the figure is about 15 yd. 2 Course Area of Irregular Figures

Example 2: Finding the Area of an Irregular Figure Find the area of the irregular figure. Use 3.14 for . Use the formula for the area of a rectangle. Substitute 8 for l. Substitute 9 for w. A = lw A = 8 9 A = 72Step 1: Separate the figure into smaller, familiar figures. 3 yd Course Area of Irregular Figures 9 yd Step 2: Find the area of each smaller figure. Area of the rectangle: 8 yd 9 yd

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

Now You Try… Find the area of the irregular figure. Use 3.14 for . Use the formula for the area of a parallelogram. Substitute 16 for b. Substitute 9 for h. A = bh A = 16 9 A = 144Step 1: Separate the figure into smaller, familiar figures. 16 m Course Area of Irregular Figures 9 m 16 m Step 2: Find the area of each smaller figure. Area of the parallelogram:

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

Additional Example 2 Continued Find the area of the irregular figure. Use 3.14 for . A ≈ = The area of the figure is about m 2. Step 3: Add the area to find the total area. 16 m Course Area of Irregular Figures 9 m 16 m

Continued Find the area of the irregular figure. Use 3.14 for . A = = 81The area of the figure is about 81 yd 2.Step 3: Add the area to find the total area. Course Area of Irregular Figures

Example 3: Finding the Shaded Region Find the area of the shaded region Use 3.14 for pi. Course Area of Irregular Figures 2 cm 4 cm Step 1: Write the formula. Step 2: Substitute values. A = area of square – area of circle A = (l x w) – ( πr 2 ) A = (4 x 4) – (3.14 x 2 2 ) A = (16) – (3.14 x 4) Step 3: Solve. A = (16) – (12.56) A = 3.44 cm 2