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10-4 Comparing Perimeter and Area Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

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Warm Up 1. What is the area of a figure made up of a rectangle with length 12 cm and height 4 cm and a parallelogram with length 12 cm and height 6 cm? 2. What is the area of a figure consisting of a triangle sitting on top of a rectangle? The triangle has a base of 12 in. and height of 9 in., and the rectangle has a base of 12 in. and height of 5 in. Course 1 10-4 Comparing Perimeter and Area 120 cm 2 114 in 2

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Problem of the Day If sixteen people sit, evenly spaced, in a circle for story time, who sits directly across from person 5? person 13 Course 1 10-4 Comparing Perimeter and Area

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Learn to make a model to explore how area and perimeter are affected by changes in the dimensions of a figure. Course 1 10-4 Comparing Perimeter and Area

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Additional Example 1: Changing Dimensions Find how the perimeter and the area of the figure change when its dimensions change. Course 1 10-4 Comparing Perimeter and Area The original figure is a 4 2 in. rectangle. The smaller figure is a 2 1 in. rectangle. Draw a model of the two figures on graph paper. Label the dimensions. = 1 inch

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Additional Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change. P = 2(l + w) = 2(4 + 2) P = 2(l + w). = 2(2 + 1) Course 1 10-4 Comparing Perimeter and Area = 2(6) = 12 = 2(3) = 6 The perimeter is 12 in. The perimeter is 6 in. Use the formula for perimeter of a rectangle. Substitute for l and w. Simplify.

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= 4 x 2 = 8 A = lw The perimeter is divided by 2, and the area is divided by 4. Course 1 10-4 Comparing Perimeter and Area A = lw = 2 The area is 8 in 2.The area is 2 in 2. Use the formula for area of a rectangle. Substitute for l and w. = 2 x 1 Simplify. Additional Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change.

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Check It Out: Example 1 Find how the perimeter and the area of the figure change when its dimensions change. Course 1 10-4 Comparing Perimeter and Area The original figure is 2 x 2 in. rectangle. The larger figure is a 4 x 4 in. rectangle. Draw a model of the two figures on graph paper. Label the dimensions. = 1 inch

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P = 2(l + w) = 2(2 + 2) P = 2(l + w). = 2(4 + 4) Course 1 10-4 Comparing Perimeter and Area = 2(4) = 8 = 2(8) = 16 The perimeter is 8 in. The perimeter is 16 in. Use the formula for perimeter of a rectangle. Substitute for l and w. Simplify. Check It Out: Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change.

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= 2 x 2 = 4 A = lw The perimeter is multiplied by 2, and the area is multiplied by 4. Course 1 10-4 Comparing Perimeter and Area A = lw = 16 The area is 4 in 2.The area is 16 in 2. Use the formula for area of a rectangle. Substitute for l and w. = 4 x 4 Simplify. Check It Out: Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change.

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Additional Example 2: Application Draw a rectangle whose dimensions are 4 times as large as the given rectangle. How do the perimeter and area change? Multiply each dimension by 4.P = 10 cm A = 6 cm 2 P = 40 cm A = 96 cm 2 When the dimensions of the rectangle are multiplied by 4, the perimeter is multiplied by 4, and the area is multiplied by 16, or 4 2. 3 cm 2 cm 8 cm 12 cm Course 1 10-4 Comparing Perimeter and Area

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Check It Out: Example 2 Draw a rectangle whose dimensions are 2 times as large as the given rectangle. How do the perimeter and area change? Multiply each dimension by 2.P = 16 cm A = 15 cm 2 P = 32 cm A = 60 cm 2 When the dimensions of the rectangle are multiplied by 2, the perimeter is multiplied by 2, and the area is multiplied by 4, or 2 2. 5 cm 3 cm 6 cm 10 cm Course 1 10-4 Comparing Perimeter and Area

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Lesson Quiz Find how the perimeter and area of the triangle change when its dimensions change. The perimeter is multiplied by 2, and the area is multiplied by 4; perimeter = 24, area = 24; perimeter = 48, area = 96. Insert Lesson Title Here Course 1 10-4 Comparing Perimeter and Area

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