Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

It takes a driver about second to begin 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? 3 4 11 ft; 22 ft; 33 ft

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.

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

Understand the Problem 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.

Additional Example 3 Continued 2 Make a Plan 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. 5 ft 8 ft 4 ft 7 ft t

Additional Example 3 Continued Solve 3 Find the area of each smaller figure. Area of the rectangle: Area of the trapezoid: A = lw A = h(b1 + b2)‏ 1 2 __ A = 8 • 5 A = • 4(5 + 7)‏ 1 2 __ A = 40 A = • 4 (12)‏ 1 2 __ Add the areas to find the total area. A = 24 A = 40 + 24 = 64 The Wrights’ need 64 ft2 of tile.

Additional Example 3 Continued 4 Look Back The area of the entry must be greater than the area of the rectangle (40 ft2), so the answer is reasonable.

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

Understand the Problem 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.

Check It Out: Example 3 Continued 2 Make a Plan 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. 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.

Check It Out: Example 3 Continued 4 Look Back The area of the wall must be greater than the area of the rectangle (108 ft2), so the answer is reasonable.