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Holt CA Course 1 10-3 Area of Parallelograms AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = d–the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Also covered: NS2.1, AF1.1, AF2.1, AF3.2 California Standards 1212

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Holt CA Course 1 10-3 Area of Parallelograms Vocabulary area base height

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Holt CA Course 1 10-3 Area of Parallelograms The area of a figure is the number of non-overlapping unit squares needed to cover the figure. Area is measured in square units. The base of a parallelogram is the length of one side. Its height is the perpendicular distance from the base to the opposite side. For a rectangle, the base is the same as the length, and the height is the same as the width. h b Area = 15 square units

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Holt CA Course 1 10-3 Area of Parallelograms

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Holt CA Course 1 10-3 Area of Parallelograms Find the area of the parallelogram. Additional Example 1: Finding the Area of a Parallelogram 8 m 16 m A = bh A = 16 · 8 A = 128 The area of the parallelogram is 128 m 2. Use the formula. Substitute for b and h. Multiply.

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Holt CA Course 1 10-3 Area of Parallelograms Find the area of the parallelogram. 6 cm 12 cm A = bh A = 12 · 6 A = 72 The area of the parallelogram is 72 cm 2. Check It Out! Example 1 Use the formula. Substitute for b and h. Multiply.

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Holt CA Course 1 10-3 Area of Parallelograms Find the area of the rectangle. Additional Example 2: Finding the Area of a Rectangle 4.5 in. 7.4 in. A = lw A = 7.4 · 4.5 A = 33.3 The area of the rectangle is 33.3 in 2. Use the formula. Substitute for l and w. Multiply.

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Holt CA Course 1 10-3 Area of Parallelograms Find the area of the rectangle. 6.3 in. 8.2 in. A = lw A = 8.2 · 6.3 A = 51.66 The area of the rectangle is 51.66 in 2. Use the formula. Substitute for l and w. Multiply. Check It Out! Example 2

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Holt CA Course 1 10-3 Area of Parallelograms The area of a playing field is 1,470 ft 2 and the length is 42 ft. What is the width of the field? Additional Example 3: Finding Length or Width of a Rectangle A = lw 1,470 = 42 · w = The width of the playing field is 35 ft. Use the formula for the area of a rectangle. Substitute 1,470 for A and 42 for l. Divide both sides by 42 to isolate w. 1,470 42 42 · w 42 35 = w

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Holt CA Course 1 10-3 Area of Parallelograms The area of a rectangular parking lot is 3,570 ft 2 and the width is 70 ft. What is the length of the parking lot? Check It Out! Example 3 A = lw 3,570 = l · 70 = The length of the parking lot is 51 ft. Use the formula for the area of a rectangle. Substitute 3,570 for A and 70 for w. Divide both sides by 70 to isolate l. 3,570 70 l · 70 70 51 = l

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Holt CA Course 1 10-3 Area of Parallelograms A carpenter is laying a wood floor measuring 4 yd by 5 yd. How many square feet of flooring material does she need? Additional Example 4: Measurement Application Step 1: Draw and label a diagram. The wood floor is measured is yards, but the answer should be in feet. 4 yd · = 12 ft 5 yd · = 15 ft Step 2: Convert the units. 4 yd 5 yd 3 ft 1 yd Convert yards to feet by multiplying by a ratio equal to 1.

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Holt CA Course 1 10-3 Area of Parallelograms A carpenter is laying a wood floor measuring 4 yd by 5 yd. How many square feet of flooring material does she need? Additional Example 4 Continued Step 3: Find the area of the floor in square feet. A = lwUse the formula for the area of a rectangle. A = 12 · 15 Substitute 12 for l and 15 for w. A = 180 Multiply. The carpenter needs 180 ft 2 of flooring material.

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Holt CA Course 1 10-3 Area of Parallelograms A carpenter is laying a tile floor measuring 5 yd by 7 yd. How many square feet of tile material does she need? Check It Out! Example 4 Step 1: Draw and label a diagram. The tile floor is measured is yards, but the answer should be in feet. 5 yd · = 15 ft 7 yd · = 21 ft Step 2: Convert the units. 5 yd 7 yd 3 ft 1 yd Convert yards to feet by multiplying by a ratio equal to 1.

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Holt CA Course 1 10-3 Area of Parallelograms Check It Out! Example 4 Continued Step 3: Find the area of the tile floor in square feet. A = lwUse the formula for the area of a rectangle. A = 15 · 21 Substitute 15 for l and 21 for w. A = 315 Multiply. The carpenter needs 315 ft 2 of tile material. A carpenter is laying a tile floor measuring 5 yd by 7 yd. How many square feet of tile material does she need?

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