Similar Shapes and Scale Drawings

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A scale drawing is proportional to a life size drawing of the same object. A scale is a ratio between two sets of measurements and is usually shown as two numbers separated by a colon. Scale drawing problems are solved using proportional reasoning and finding equivalent ratios. Changing the scale of a drawing to a new scale with larger numbers will decrease the size of the drawing, not increase it. Scale drawings have many applications in everyday life.

Charlie and Zachery are each making a scale drawing of the school garden. The garden measures 30 feet by 12 feet. Charlie plans to use a scale of 1 inch: 2 feet. Zachery plans to use a scale of 2 inches: 1 foot. Which is the better plan? Justify your answer.

You use scale drawings to represent measurements of actual objects or places. You can find dimensions of actual objects by making and completing a table or by writing and solving proportions. A scale drawing must be proportional to a life-size drawing of the same object. Since a scale drawing and a life-size drawing are proportional, they are similar: any corresponding angles will have equivalent measures, and the ratios of the lengths of corresponding sides are proportional.

Are the scales 2 in.:3 ft. and 1:18 the same scale? Explain.

Can you multiply the numerator and denominator of 2 𝑖𝑛. 3 𝑓𝑡 Can you multiply the numerator and denominator of 2 𝑖𝑛. 3 𝑓𝑡. by the same number to show 2 𝑖𝑛. 3 𝑓𝑡. = 11 𝑖𝑛. 16.5 𝑓𝑡. ? Explain.

How can you use a scale to determine whether the drawing or the object is larger? Put both parts of the scale in the same unit. If the first number is greater, then the drawing is larger. If the second number is greater, then the object is larger.

Joanne has a scale drawing of her backyard that includes a garden bed that measures 25 inches long and 16 inches wide. What is the area of the actual garden bed?

How do you use the scale on a scale drawing to find the measurements of the actual object? Write the scale as a ratio in fraction form. Use the ratio to write a proportion that uses measurements from the scale drawing. Use proportional reasoning to solve for the actual measurements in the proportion.

The scale in the drawing is 2 in. :4 ft The scale in the drawing is 2 in.:4 ft. What are the length and width of the actual room? Find the area of the actual room.

The scale in the drawing is 2 cm:5 m The scale in the drawing is 2 cm:5 m. What are the length and width of the actual room? Find the area of the actual room.

The area of a square floor on a scale drawing is 100 square centimeters, and the scale of the drawing is 1 cm:2 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?

A billboard is 2. 5 times as long as it is wide A billboard is 2.5 times as long as it is wide. The area of the billboard is 2,250 𝑓𝑡 2 . A scale drawing is made of the billboard, and the area of the scale drawing is 160 𝑖𝑛 2 . What is the scale used in the scale drawing? Explain.

Exit Ticket A scale drawing of a billboard uses the scale 4 cm:9 ft. The length of the billboard in the drawing is 11 cm. How long is the actual billboard? A scale drawing of a dance floor is shown. What is the area of the actual dance floor? A bookcase measures 13 feet wide and 24 feet tall. What would the bookcase’s measurements be on a scale drawing using the scale 3 cm:2 ft? Bob makes a scale drawing of a statue using the scale 1cm:5 ft. His drawing measures 12 cm. Kia makes a scale drawing of the same statue using the scale 1cm:4 ft. How many centimeters tall is the statue in Kia’s drawing?