2)The length of each side in Drawing 1 is 12 units, and the length of each side in Drawing 2 is 6 units. Scale Factor: Scale Factor
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1 Lesson Date Solving Area Problems Using Scale Drawings Student Objective I can solve area problems related to scale drawings and percent by using the fact that an areaof a scale drawing is the area of the original drawing times the square of the scale factor. Classwork Opening Exercise For each diagram, Drawing 2 is a scale drawing of Drawing 1. Complete the accompanying charts. For each drawing: identify the side lengths, determine the area, and compute the scale factor. Convert each scale factor into a fraction and percent, examine the results, and write a conclusion relating scale factors to area. 1) 2)The length of each side in Drawing 1 is 12 units, and the length of each side in Drawing 2 is 6 units. Side Drawing 1 Drawing 2 Scale Factor as a Fraction and Percent Side Drawing 1 Drawing 2 Scale Factor as a Fraction and Percent Area Area Scale Factor: Quotient of Areas: Scale Factor: Quotient of Areas: Conclusion:
2 Example 1 What percent of the area of the large square is the area of the small square? Exercises 1. The Lake Smith basketball team had a team picture taken of the players, the coaches, and the trophies from the season. The picture was 4 inches by 6 inches. The team decides to have the picture enlarged to a poster and then enlarged again to a banner measuring 48 inches by 72 inches. a. Sketch and label drawings to illustrate the original picture and enlargements. b. If the scale factor from the picture to the poster is 500%, determine the dimensions of the poster. c. What scale factor is used to create the banner from the picture? d. What percent of the area of the picture is the area of the poster? Justify your answer using the scale factor AND by finding the actual areas.
3 e. Write an equation involving the scale factor that relates the area of the poster to the area of the picture. f. Assume you started with the banner and wanted to reduce it to the size of the poster. What would the scale factor as a percent be? g. What scale factor would be used to reduce the poster to the size of the picture? Lesson Summary If the scale factor is represented by k, then the area of the scale drawing is k 2 times the corresponding area of the original drawing.
4 Math 7 Period Homework Set Name Date Homework Homework Homework Homework Homework 1. Ben cut the following rockets out of cardboard. The height from the base to the tip of the smaller rocket is 20 cm. The height from the base to the tip of the larger rocket is 120 cm. What percent of the area of the smaller rocket is the area of the larger rocket?(pictures not drawn to scale!) 2. In the photo frame depicted below, three 5 inch by 5 inch squares are cut out for photographs. These cutout regions make up 16of the area of the entire photo frame.(picture not drawn to scale!) 3 a. What fraction of the entire area does just one cut-out region represent? b. What is the scale factor between the area of the smaller square and the area of the larger square? c. What is the scale factor between the side length of a smaller scale and the side length of the larger square? d. What are the dimensions of the photo frame?
5 6 in. 10 in. 3. Kelly was online shopping for envelopes for party invitations and saw these images on a website. The website listed the dimensions of the small envelope as 6 in. by 8 in. and the medium envelope as 10 in. by 1 13 in. 3 8 in in. a. Compare the dimensions of the small and medium envelopes. If the medium envelope is a scale drawing of the small envelope, what is the scale factor? b. If the large envelope was created based on the dimensions of the small envelope using a scale factor of 250%, find the dimensions of the large envelope. c. If the medium envelope was created based on the dimensions of the large envelope, what scale factor was used to create the medium envelope? d. What percent of the area of the larger envelope is the area of the medium envelope?
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