9-6 Area of Irregular Figures 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 m in yd 2

9-6 Area of Irregular Figures Problem of the Day It takes a driver about second to begin breaking after seeing something in the road. How many feet does a car travel in that time if it is going 10 mph? 20 mph? 30 mph? 11 ft; 22 ft; 33 ft 3434

9-6 Area of Irregular Figures Vocabulary composite figure Learn to find the area of irregular figures.

9-6 Area of Irregular Figures 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.

9-6 Area of Irregular Figures 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) = = The area of the figure is about 50 yd 2.

9-6 Area of Irregular Figures 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) = = The area of the figure is about 15 yd. 2

9-6 Area of Irregular Figures Additional 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 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 9 m 16 m Step 2: Find the area of each smaller figure. Area of the parallelogram:

9-6 Area of Irregular Figures Additional Example 2 Continued Find the area of the irregular figure. Use 3.14 for . Substitute 3.14 for  and 8 for r. 16 m 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 ≈

9-6 Area of Irregular Figures 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 9 m 16 m

9-6 Area of Irregular Figures Check It Out: Example 2 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 9 yd Step 2: Find the area of each smaller figure. Area of the rectangle: 8 yd 9 yd

9-6 Area of Irregular Figures Check It Out: Example 2 Continued Find the area of the irregular figure. Use 3.14 for . Substitute 2 for b and 9 for h. 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

9-6 Area of Irregular Figures Check It Out: Example 2 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.

9-6 Area of Irregular Figures Additional Example 3: Problem Solving Application The Wrights want to tile their entry with one-square-foot tiles. How much tile will they need? 5 ft 8 ft 4 ft 7 ft t

9-6 Area of Irregular Figures Additional Example 3 Continued 1 Understand the Problem Rewrite the question as a statement. Find the amount of tile needed to cover the entry floor. List the important information: The floor of the entry is an irregular shape. The amount of tile needed is equal to the area of the floor.

9-6 Area of Irregular Figures Additional Example 3 Continued Find the area of the floor by separating the figure into familiar figures: a rectangle and a trapezoid. Then add the areas of the rectangle and trapezoid to find the total area. 2 Make a Plan 5 ft 8 ft 4 ft 7 ft t

9-6 Area of Irregular Figures Additional Example 3 Continued Solve 3 Find the area of each smaller figure. A = lw A = 8 5 A = 40Area of the rectangle: Area of the trapezoid: A = 24 A = h(b 1 + b 2 ) ‏ 1 2 __ A = 4(5 + 7) ‏ 1 2 __ A = 4 (12) ‏ 1 2 __ Add the areas to find the total area. A = = 64The Wrights’ need 64 ft 2 of tile.

9-6 Area of Irregular Figures Additional Example 3 Continued Look Back 4 The area of the entry must be greater than the area of the rectangle (40 ft 2 ), so the answer is reasonable.

9-6 Area of Irregular Figures 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

9-6 Area of Irregular Figures Check It Out: Example 3 Continued 1 Understand the Problem Rewrite the question as a statement. Find the amount of wallpaper needed to cover the loft wall. List the important information: The wall of the loft is an irregular shape. The amount of wallpaper needed is equal to the area of the wall.

9-6 Area of Irregular Figures Check It Out: Example 3 Continued Find the area of the wall by separating the figure into familiar figures: a rectangle and a triangle. Then add the areas of the rectangle and triangle to find the total area. 2 Make a Plan 6 ft 23 ft 18 ft 5 ft

9-6 Area of Irregular Figures Check It Out: Example 3 Continued Solve 3 Find the area of each smaller figure. A = lw A = 18 6 A = 108Area of the rectangle: Area of the triangle: Add the areas to find the total area. A = = 135.5The Franklins need ft 2 of wallpaper.A = 27.5 A = bh 1 2 __ A = (5 11) ‏ 1 2 __ A = (55) ‏ 1 2 __

9-6 Area of Irregular Figures Check It Out: Example 3 Continued Look Back 4 The area of the wall must be greater than the area of the rectangle (108 ft 2 ), so the answer is reasonable.

9-6 Area of Irregular Figures 1. Identify the perimeter and area of the figure. A. 50 cm; 42 cm 2 B. 50 cm; 54 cm 2 C. 34 cm; 54 cm 2 D. 34 cm; 42 cm 2 Lesson Quiz for Student Response Systems

9-6 Area of Irregular Figures 2. Identify the perimeter and area of the figure. A in.; in 2 B in.; in 2 C in.; in 2 D in.; in 2 Lesson Quiz for Student Response Systems