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10-4 Comparing Perimeter and Area Warm Up Problem of the Day Lesson Presentation Course 1 10-4 Comparing Perimeter and Area 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 120 cm2 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. 114 in2 Course 1 10-4 Comparing Perimeter and Area 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 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 Additional Example 1: Changing Dimensions Find how the perimeter and the area of the figure change when its dimensions change. = 1 inch Draw a model of the two figures on graph paper. Label the dimensions. The original figure is a 4 2 in. rectangle. Course 1 The smaller figure is a 2 1 in. rectangle. 10-4 Comparing Perimeter and Area Additional Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change. Use the formula for perimeter of a rectangle. P = 2(l + w) P = 2(l + w). Substitute for l and w. = 2(4 + 2) = 2(2 + 1) Simplify. = 2(6) = 12 The perimeter is 12 in. Course 1 = 2(3) = 6 The perimeter is 6 in. 10-4 Comparing Perimeter and Area Additional Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change. Use the formula for area of a rectangle. A = lw A = lw Substitute for l and w. =4x2 =8 Simplify. The area is 8 in2. =2x1 =2 The area is 2 in2. The perimeter is divided by 2, and the area is divided by 4. Course 1 10-4 Comparing Perimeter and Area Check It Out: Example 1 Find how the perimeter and the area of the figure change when its dimensions change. = 1 inch Draw a model of the two figures on graph paper. Label the dimensions. The original figure is 2 x 2 in. rectangle. Course 1 The larger figure is a 4 x 4 in. rectangle. 10-4 Comparing Perimeter and Area Check It Out: Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change. Use the formula for perimeter of a rectangle. P = 2(l + w) P = 2(l + w). Substitute for l and w. = 2(2 + 2) = 2(4 + 4) Simplify. = 2(4) = 8 The perimeter is 8 in. Course 1 = 2(8) = 16 The perimeter is 16 in. 10-4 Comparing Perimeter and Area Check It Out: Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change. Use the formula for area of a rectangle. A = lw A = lw Substitute for l and w. =2x2 =4 Simplify. The area is 4 in2. =4x4 = 16 The area is 16 in2. The perimeter is multiplied by 2, and the area is multiplied by 4. Course 1 10-4 Comparing Perimeter and Area 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? 12 cm 2 cm 3 cm 8 cm Multiply each dimension by 4. P = 10 cm P = 40 cm A = 6 cm2 A = 96 cm2 When the dimensions of the rectangle are multiplied by 4, the perimeter is multiplied by 4, and the area is multiplied by 16, or 42. Course 1 10-4 Comparing Perimeter and Area 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? 10 cm 5 cm 6 cm 3 cm Multiply each dimension by 2. P = 16 cm P = 32 cm A = 15 cm2 A = 60 cm2 When the dimensions of the rectangle are multiplied by 2, the perimeter is multiplied by 2, and the area is multiplied by 4, or 22. Course 1 10-4 Comparing Insert Lesson Perimeter Title Here and Area 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. Course 1