Similar Shapes and Scale Drawings Warm Up A

Similar Shapes and Scale Drawings

Warm Up

• 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 lifesize 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.

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. 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. 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?

Exit Ticket 1. 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? 2. A scale drawing of a dance floor is shown. What is the area of the actual dance floor? 3. 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? 4. Bob makes a scale drawing of a statue using the scale 1 cm: 5 ft. His drawing measures 12 cm. Kia makes a scale drawing of the same statue using the scale 1 cm: 4 ft. How many centimeters tall is the statue in Kia’s drawing?