![]() When you make a photocopy of an image, is the photocopy a dilation? What is the scale factor? How do the perimeter and area change? 8. When a rectangle is dilated, how do the perimeter and area of the rectangle change? 378 Unit 5ĥ Name Class Date 13.3 Independent Practice 8.3.B, 8.10.A, 8.10.B, 8.10.D Personal Math Trainer Online Assessment and Intervention 7. What is the area of the soccer field in the back yard? ESSENTIAL QUESTION CHECK-IN 6. What is the scale factor of the dilation? 5. What is the perimeter of the full-size soccer field? 4. To fit the field in the back yard, the group needs to reduce the size of the field so its perimeter is 128 yards. A full-size soccer field is a rectangle with a length of 100 yards and a width of 60 yards. Scale factor = Scale factor = 3 _ P = 48 A = 128 P = 12 A = 9 P' = A' = P' = A' = A group of friends is roping off a soccer field in a back yard. What is the area of the original artwork? Guided Practice Find the perimeter and area of the image after dilating the figures shown with the given scale factor. The perimeter of the original artwork is 136 inches. The rectangular mouse pads are dilated from the original artwork and have a length of 9 inches and a width of 8 inches. Johnson Middle School is selling mouse pads that are replicas of a student s award-winning artwork. LessonĤ YOUR TURN Personal Math Trainer Online Assessment and Intervention 2. ![]() The length of the mini-card is l s 1_ 2 = 3.5 1_ 2 = 1.75 in., and the width is w s 1_ 2 = 2.5 1_ 2 = 1.25 in. Justify and Evaluate To find the area of the mini-card, find its length and width by multiplying the dimensions of the standard card by the scale factor. The area of the mini card is about 2.2 square inches. A m = A s k 2 A m = 8.75 ( 1_ 2) 2 A m = _ 4 A m = in 2 Multiply the area of the standard card by the scale factor squared to get the area of the mini-card. A s = 8.75 in 2 STEP 4 Find the area of the mini-card. ![]() A s = l s w s A s = Use the formula for the area of a rectangle. STEP 3 Find the area of the standard card. P m = P s k 6 = 12 k 1_ 2 = k Multiply the perimeter of the standard card by the scale factor to get the perimeter of the mini-card. ![]() Justify Solve and Evaluate STEP 1 Find the perimeter of the standard card. Then use the scale factor to find the area of the mini-card. Find the perimeter of the standard card, and use that to find the scale factor. 8.3.B Image Credits: Stockbyte/ Getty Images 376 Unit 5ģ Formulate a Plan My Notes Since the mini-card is a dilation of the standard card, the figures are similar. I know the length and width of a standard card and the perimeter of a mini-card. What is the area of a card in the mini-deck? Analyze Information I need to find the area of a mini-card. The perimeter of a card in the mini-deck is 6 inches. A card in the standard deck is a rectangle that has a length of 3.5 inches and a width of 2.5 inches. EXAMPLE 1 Problem Solving A souvenir shop sells standard-sized decks of cards and mini-decks of cards. How are the perimeter and area of a dilated figure related to the perimeter and area of the original figure? Perimeter Area Original 8 4 Dilation Perimeter Area Original Dilation Scale factor = 2 Scale factor = 1_ 6 Math On the Spot Animated Math Problem-Solving Application Understanding how dilations affect the linear and area measurements of shapes will enable you to solve many real-world problems. Make a Conjecture The perimeter and area of two shapes before and after dilation are given. A' A D B C B' AB = BC = CD = DA = A'B' = B'C' = C'D' = D'A' = D' C' A'B' AB = B'C' BC = C'D' CD = What is true about the ratios that you calculated? D'A' DA = B What scale factor was used to dilate the green rectangle to the blue rectangle? How are the side lengths of the blue rectangle related to the side lengths of the green rectangle? What is the perimeter of the green rectangle? What is the perimeter of the blue rectangle? How is the perimeter of the blue rectangle related to the perimeter of the green rectangle? LessonĢ EXPLORE ACTIVITY (cont d) C What is the area of the green rectangle? What is the area of the blue rectangle? How is the area of the blue rectangle related to the area of the green rectangle? Reflect 1. Then calculate the ratios of all pairs of corresponding sides. A Using a centimeter ruler, measure and record the length of each side of both rectangles. Also 8.3.B, 8.10.A, 8.10.B? ESSENTIAL QUESTION How do you describe the effects of dilation on linear and area measurements? EXPLORE ACTIVITY 8.10.D Exploring Dilations and Measurement The blue rectangle is a dilation (enlargement) of the green rectangle. 1 LESSON 13.3 Dilations and Measurement Two-dimensional shapes 8.10.D Model the effect on linear and area measurements of dilated two-dimensional shapes.
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