9-3 Area of Irregular Figures Formulas for 9.3 Area of a rectangle: A= lw Area of a triangle: Area of a trapezoid: Area of a parallelogram: A=bh

9-3 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

9-3 Area of Irregular Figures Today’s Goal: Learn to find the area of irregular figures.

9-3 Area of Irregular Figures Vocabulary composite figure

9-3 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.

9-3 Area of Irregular Figures Estimating the Area Do not write, watch only 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

9-3 Area of Irregular Figures Estimating the Area of an Irregular Figure Don’t write anything, watch only 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.

9-3 Area of Irregular Figures Example 1: 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:

9-3 Area of Irregular Figures Example 1 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 2 ) ‏ 1 2 __ The area of a semicircle is the area of a circle A ≈ ( ) ‏ 1 2 __ A ≈ (200.96) 1 2 __ Multiply. A ≈

9-3 Area of Irregular Figures Example 1 Continued Find the area of the irregular figure. 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

9-3 Area of Irregular Figures Example 2 Find the area of the irregular figure. Use the formula for the area of a rectangle. Substitute 8 for l. Substitute 9 for w. A = lw A = 8 9 A = 72 yd 2 Step 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

9-3 Area of Irregular Figures Example 2 Continued Find the area of the irregular figure. Substitute 3 for b and 9 for h. Area of the triangle: A = bh 1 2 __ The area of a triangle is the b h A = (3 9) ‏ 1 2 __ A = (27) 1 2 __ Multiply. A = 13.5 yd 2 3 yd 9 yd 8 yd 9 yd

9-3 Area of Irregular Figures Example 2 Continued Find the area of the irregular figure. A = = 85.5The area of the figure is about 85.5 yd 2.Step 3: Add the area to find the total area.

9-3 Area of Irregular Figures Example 3: Problem Solving Application Don’t write; watch only 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

9-3 Area of Irregular Figures 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.

9-3 Area of Irregular Figures 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

9-3 Area of Irregular Figures Example 3 Continued Solve 3 Find the area of each smaller figure. A = lw A = 8 5 A = 40 Area 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.

9-3 Area of Irregular Figures Today’s assignments: Use a separate sheet of paper for each assignment pg (skip #6), 20, 22 Include an answer key and labels for every problem pg evens only (note-#14 has two answers) Include an answer key and labels for every problem These problems have MULTIPLE parts-even with a calculator, you should have a lot of work written down, including the formulas you are using! Done? Choose an irregular shape card from the green counter and try to solve the area. You can write directly on the picture. When finished, check your answer with the green answer sheet. Then, try another card!

9-3 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.

9-3 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

9-3 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.

9-3 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

9-3 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 __

9-3 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.