8 3 Area of Rectangles and Parallelograms Learn

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 halffull: 4 green squares = 2 full squares. Do not count almost empty yellow squares. Add. 19 + 2 = 30 2 The area of the figure is about 30 mi.

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 halffull: 4 blue squares = 2 full = mi 2 squares. Do not count almost empty yellow squares. Add. 11 + 5 + 2 = 18 The area of the figure is about 18 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. 15 in. 9 in. A = lw A = 15 Write the formula. • A = 135 9 Substitute 15 for l. Substitute 9 for w. The area is about 135 in 2.

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

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. A = bh 1 1 ft 4 2 1 ft 2 Write the formula. 1 __ 1 1 __ __ Substitute 2 for b 2 A = 2 2 • 14 1 __ and 1 for h. 4 5 5 __ __ A= • Multiply. 2 4 25 1 ___ __ A= or 3 8 8 1 2 __ The area is 3 ft. 8

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

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? To find the area to be tiled, subtract the area of the island from the area of the floor area �– island = kitchen area to be tiled (13 • 17) – (3 • 6) = n 221 – 18 = 203 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.

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? To find the landscaped area, subtract the area of the BBQ from the area of the backyard. = landscaped area backyard area – BBQ Substitute for l and w in A = lw. 176 – 8 = 168 Use the order of operations. The area of the backyard to be landscaped is 168 ft 2. (16 • 11) – (2 • 4) = n