Changing Dimensions: Perimeter and Area. Additional Example 1: Comparing Perimeters and Areas Find how the perimeter and the area of the figure change.

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Presentation transcript:

Changing Dimensions: Perimeter and Area

Additional Example 1: Comparing Perimeters and Areas Find how the perimeter and the area of the figure change when its dimensions change. 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

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) = 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.

= 4 x 2 = 8 A = lw The perimeter is divided by 2, and the area is divided by 4. 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.

Check It Out: Example 1 Find how the perimeter and area of the figure change when its dimensions change. 8 in. 4 in. 2 in.

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 cm 2 cm 8 cm 12 cm

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?

Additional Example 3: Application Mei works at a local diner whose speciality is making pancakes. She makes silver dollar pancakes with a diameter of 2 inches as well as regular pancakes with a diameter double that of the silver dollar pancakes. Does a regular pancake have twice the area of a silver dollar pancake? Explain. Use 3.14 for . Find the area of each pancake and compare. Silver: A = r 2 Regular: A = r 2 Use the formula. A  (1)2A  (1)2 A  (2)2A  (2)2 Substitute for r. A    1A    4 Evaluate the power. A  3.14A  Multiply.

Additional Example 3 Continued Mei works at a local diner whose speciality is making pancakes. She makes silver dollar pancakes with a diameter of 2 inches as well as regular pancakes with a diameter double that of the silver dollar pancakes. Does a regular pancake have twice the area of a silver dollar pancake? Explain. Use 3.14 for . The area of the silver dollar pancake is 3.14 in 2, and the area of the regular pancake is in 2. When the diameter is doubled, the area is 2 2, or 4, times as great.

Check It Out: Example 3 Rae is designing a can for a new line of soup products. The original can had a base diameter of 7 cm and her new design will be double that of the original base diameter. Will the new soup can take up double the shelf space of the original can? Explain. Use 3.14 for .