A rectangular scale drawing is 4 cm by 6 cm. The scale is 1 cm = 2 yd. Find the actual dimensions and area.
Show reasoning / computation: __________________________________________
CCSS 7.G.A.1 · scale drawings, lengths & areas
Scale Drawing Length and Area Worksheet Generator
Practice using a scale to move between drawing dimensions and real dimensions, then extend the reasoning to area. Every rectangle diagram is generated from the same dimensions used in the answer key, so the visual and calculation cannot drift apart.
Preview · US Letter
Scale Drawing Lengths & Areas
Diagrams are part of the problem data, not decorative assets. Student pages keep solution-specific marks hidden; reveal answers or use the separate PDF key to check work.
Problem 1
Problem 2
A rectangular scale drawing is 6 cm by 5 cm. The scale is 1 cm = 3 yd. Find the actual dimensions and area.
Show reasoning / computation: __________________________________________
Problem 3
A rectangular scale drawing is 6 cm by 5 cm. The scale is 1 cm = 4 ft. Find the actual dimensions and area.
Show reasoning / computation: __________________________________________
Problem 4
A rectangular scale drawing is 2 cm by 4 cm. The scale is 1 cm = 4 m. Find the actual dimensions and area.
Show reasoning / computation: __________________________________________
Problem 5
A rectangular scale drawing is 2 cm by 4 cm. The scale is 1 cm = 3 yd. Find the actual dimensions and area.
Show reasoning / computation: __________________________________________
Problem 6
A rectangular scale drawing is 6 cm by 5 cm. The scale is 1 cm = 8 yd. Find the actual dimensions and area.
Show reasoning / computation: __________________________________________
Problem 7
A rectangular scale drawing is 7 cm by 5 cm. The scale is 1 cm = 4 m. Find the actual dimensions and area.
Show reasoning / computation: __________________________________________
Problem 8
A rectangular scale drawing is 2 cm by 4 cm. The scale is 1 cm = 6 yd. Find the actual dimensions and area.
Show reasoning / computation: __________________________________________
Finding actual lengths and areas from a scale drawing
To find an actual length, multiply the drawing length by the scale. Areas work differently: if lengths are scaled by a factor of k, areas are scaled by k × k, so the area scale factor is the square of the length scale factor. Compute the actual lengths first and then the area, or use the squared factor.
Worked examples
- At 1 cm : 3 m, a 5 cm side is 15 m long.
- A 4 cm by 2 cm drawn rectangle at 1 cm : 3 m is 12 m by 6 m, so its actual area is 72 m².
- A length scale of 1 : 3 gives an area scale of 1 : 9, since 3 × 3 = 9. A 2 cm² drawn area stands for 18 cm² in the same units.
Common slips
- Multiplying an area by the length scale only. With a length factor of 3, the area factor is 9.
- Forgetting the square units. Area is in m², not m.
- Using the drawing area as the real area without scaling.
How to use this worksheet
Ask students to find the actual lengths before the area and to check that the area is the product of the two actual lengths. The answer key lists the lengths and the area.
Common Core connection
- 7.G.A.1 · Solve problems involving scale drawings, including finding actual or drawing lengths.
- 7.G.B.6 · Solve problems involving area, surface area, and volume using known formulas.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Teaching note 1
A length scale factor multiplies every corresponding length.
Teaching note 2
Area does not scale by the same factor as length; it scales by the square of the length factor.
Teaching note 3
Example: at a scale of 1 cm to 4 m, a 5 cm drawing length is 20 m, and because the area factor is 4 squared, 3 square cm on paper is 48 square m.
Teaching note 4
Keep drawing units and real-world units separate until the conversion is complete.
Continue the 7.G progression
Move to another Grade 7 geometry skill
Frequently asked questions
Do these include area scale factors?
Yes. Answer keys explicitly distinguish the length scale factor from the squared area factor.
Are the rectangles drawn from the generated dimensions?
Yes. The preview and PDF diagram use the same width, height, and scale data as the problem and answer.
Which standard does this practice?
CCSS 7.G.A.1: solve problems involving scale drawings, including computing actual lengths and areas from a scale drawing.