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Similar Shapes Scale Drawings
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Similar Shapes Scale Drawings
Carlos, Ravi, and Chloe are planning a new ice rink. Use scale factors and proportional sides to check their designs. Show calculations where asked. Remember: similar shapes have equal corresponding angles and proportional corresponding sides.
Scale Factors and Similarity
Use scale drawings to compare lengths and shapes.
1.On a rink blueprint, 1 inch represents 8 feet. A real rink wall is 48 feet long. How long should that wall be on the blueprint?
- 6 inches
- 8 inches
- 40 inches
- 56 inches
2.A small rink model is similar to the full rink. The scale factor from the full rink to the model is 1:16. If the full rink is 48 feet long, what is the model's length in feet?
3.Select all statements that must be true for two polygons to be similar.
- Corresponding angles have equal measures.
- Corresponding side lengths have the same ratio.
- Every corresponding side has the same length.
- One shape can be enlarged or reduced to match the other.
4.A rectangular sign is 3 feet wide and 2 feet tall. Chloe makes a similar drawing that is 9 inches wide. What is the drawing's height?
Read the Rink Plan
For Questions 5–7, use the dimensions and scale stated in each question.
5.The rink is labeled 48 feet by 24 feet. What should its dimensions be on a drawing that uses 1 inch = 8 feet?
6.The equipment area is labeled 12 feet by 8 feet. Find its drawing dimensions using the same scale, 1 inch = 8 feet.
7.Ravi says the rink drawing should be 6 inches by 3 inches because the real rink is 48 feet by 24 feet. Explain why both dimensions use the same scale factor and how the drawing keeps the rink's shape.
Plan and Check
Apply the scale ideas to a new rink feature.
8.Carlos wants a similar rink drawing that is 9 inches long. The real rink is 48 feet long and 24 feet wide. What should the drawing's width be, and what scale does the drawing use?
9.Design your own scale drawing of a rectangular skate-storage area that is 20 feet long and 12 feet wide. Choose a scale that makes both drawing dimensions whole inches. State your scale, calculate the drawing dimensions, and sketch the rectangle.
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