# 8-3 Area of Rectangles and Parallelograms Learn to estimate the area of irregular figures and to find the area of rectangles and parallelograms.

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8-3 Area of Rectangles and Parallelograms Learn to estimate the area of irregular figures and to find the area of rectangles and parallelograms.

8-3 Area of Rectangles and Parallelograms Vocabulary area

8-3 Area of Rectangles and Parallelograms The area of a figure is the amount of surface it covers. We measure area in square units.

8-3 Area of Rectangles and Parallelograms Additional Example 1: Estimating the Area of an Irregular Figure Find the area of the rectangle. Count full squares: 19 red squares. Count almost-full squares: 9 blue squares. Count squares that are about half- full: 4 green squares = 2 full squares. Do not count almost empty yellow squares. Add. 19 + 9 + 2 = 30 The area of the figure is about 30 mi. 2

8-3 Area of Rectangles and Parallelograms Check It Out: Example 1 Estimate the are of the figure. Count full squares: 11 red squares. Count almost-full squares: 5 green squares. Count squares that are about half- full: 4 blue squares = 2 full squares. Do not count almost empty yellow squares. Add. 11 + 5 + 2 = 18 The area of the figure is about 18 mi 2. = mi 2

8-3 Area of Rectangles and Parallelograms

8-3 Area of Rectangles and Parallelograms Additional Example 2: Finding the Area of a Rectangle Find the area of the figure. Write the formula. Substitute 15 for l. Substitute 9 for w. A = lw A = 15 9 A = 135 The area is about 135 in 2. 15 in. 9 in.

8-3 Area of Rectangles and Parallelograms Check It Out: Example 2 Find the area of the figure. Write the formula. Substitute 13 for l. Substitute 7 for w. A = lw A = 13 7 A = 91 The area is about 91 in 2. 13 in. 7 in.

8-3 Area of Rectangles and Parallelograms You can use the formula for the area of a rectangle to write a formula for the area of a parallelogram. Imagine cutting off the triangle drawn in the parallelogram and sliding it to the right to form a rectangle. The area of a parallelogram = bh. The area of a rectangle = lw. The base of the parallelogram is the length of the rectangle. The height of the parallelogram is the width of the rectangle.

8-3 Area of Rectangles and Parallelograms Additional Example 3: Finding the Area of a Parallelogram Find the area of the parallelogram. Write the formula. Multiply. A = bh 2 ft 1 2 A = 2 1 1 2 __ 1 4 Substitute 2 for b and 1 for h. 1 2 __ 1 4 A = 5 2 __ 5 4 A = or 3 25 8 ___ 1 8 __ The area is 3 ft 2. 1 8 __ 1 4 1 ft

8-3 Area of Rectangles and Parallelograms Check It Out: Example 3 Find the area of the parallelogram. Write the formula. Multiply. A = bh A = 1 3 1 2 __ 1 2 Substitute 1 for b and 3 for h. 1 2 __ 1 2 A = 3 2 __ 7 2 A = or 5 21 4 ___ 1 4 __ The area is 5 ft 2. 1 4 __ 1 1 ft 2 1 3 ft 2

8-3 Area of Rectangles and Parallelograms Additional Example 4: Recreation Application Jessika is going to tile a kitchen that measures 13 ft by 17 ft. Some floor space is taken up by an island that measures 3 ft by 6 ft. How much area remains to be tiled in the kitchen? Substitute for l and w in A = lw. Use the order of operations. The area of the kitchen to be tiled is 203 ft 2. floor area To find the area to be tiled, subtract the area of the island from the area of the floor. kitchen area to be tiledisland ––= (13 17) ‏ (3 6) ‏ n –= 221 – 18 = 203

8-3 Area of Rectangles and Parallelograms Check It Out: Example 4 Miguel is going to landscape his backyard that measures 16 ft by 11 ft. Some of the backyard space is taken up by a built-in BBQ that measures 2 ft by 4 ft. How much area remains to be landscaped? Substitute for l and w in A = lw. Use the order of operations. The area of the backyard to be landscaped is 168 ft 2. backyard area To find the landscaped area, subtract the area of the BBQ from the area of the backyard. landscaped areaBBQ –= (16 11) ‏ (2 4) ‏ n –= 176 – 8 = 168

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