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

Area of Irregular Figures Course 2 9-6 Area of Irregular Figures 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 m2 540 in2 4 yd2

Area of Irregular Figures Course 2 9-6 Area of Irregular Figures Learn to find the area of irregular figures.

Area of Irregular Figures Course 2 9-6 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.

Area of Irregular Figures Course 2 9-6 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) = 11 + 4 =15. 1 2 The area of the figure is about 15 yd . 2

Find the area of the irregular figure. Use 3.14 for p. Course 2 9-6 Area of Irregular Figures Example 2: Finding the Area of an Irregular Figure Find the area of the irregular figure. Use 3.14 for p. 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

Area of Irregular Figures Course 2 9-6 Area of Irregular Figures Continued Find the area of the irregular figure. Use 3.14 for p. Area of the triangle: 8 yd 9 yd The area of a triangle is the b • h. 12 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.

Area of Irregular Figures Course 2 9-6 Area of Irregular Figures Now You Try… Find the area of the irregular figure. Use 3.14 for p. 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

Area of Irregular Figures Course 2 9-6 Area of Irregular Figures Continued Find the area of the irregular figure. Use 3.14 for p. 16 m Area of the semicircle: 9 m The area of a semicircle is the area of a circle. 12 A = (pr) 1 2 __ 16 m A ≈ (3.14 • 82) 1 2 __ Substitute 3.14 for p and 8 for r. A ≈ (200.96) 1 2 __ A ≈ 100.48 Multiply.

Additional Example 2 Continued Course 2 9-6 Area of Irregular Figures Additional Example 2 Continued Find the area of the irregular figure. Use 3.14 for p. 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.

Area of Irregular Figures Course 2 9-6 Area of Irregular Figures Continued Find the area of the irregular figure. Use 3.14 for p. Step 3: Add the area to find the total area. A = 72 + 9 = 81 The area of the figure is about 81 yd2.

Example 3: Finding the Shaded Region Course 2 9-6 Area of Irregular Figures Example 3: Finding the Shaded Region Find the area of the shaded region Use 3.14 for pi. Step 1: Write the formula. A = area of square – area of circle A = (l x w) – ( πr2) 4 cm Step 2: Substitute values. 2 cm A = (4 x 4) – (3.14 x 22) Step 3: Solve. A = (16) – (3.14 x 4) A = (16) – (12.56) 4 cm A = 3.44 cm2