7.G.A.1 7th Grade Geometry

Scale Drawings

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas and reproducing a drawing at a different scale.

How to explain it

At this standard, students use scale factors to find actual measurements, drawing measurements, and the scale itself.

The anchor students hold onto: drawing × scale = actual. Rearrange: actual ÷ scale = drawing; actual ÷ drawing = scale.

Scale factors return in 8th grade as dilations on the coordinate plane, where this same constant of proportionality maps a figure to a similar one with proportional side lengths.

Worked examples

Example 1 Find the Actual

Find actual: 4×3 cm, 1 cm=2 m.

Step 1Length: 4 cm × 2 = 8 m.

Step 2Width: 3 cm × 2 = 6 m.

Step 3Actual: 8 m × 6 m.

Step 4k = 200 (1:200 scale).

Answer8 m × 6 m

Example 2 Find the Drawing

Find drawing: 8×6 m, 1 cm=2 m.

Step 1Length: 8 m ÷ 2 = 4 cm.

Step 2Width: 6 m ÷ 2 = 3 cm.

Step 3Drawing: 4 cm × 3 cm.

Step 4Same k = 200 thread.

Answer4 cm × 3 cm

Example 3 Find the Scale

Find scale: 4 cm → 8 m.

Step 1Compare: 8 m ÷ 4 cm.

Step 2Reduce: 1 cm to 2 m.

Step 3Scale: 1 cm = 2 m.

Step 4k = 200 confirmed.

Answer1 cm = 2 m (k = 200)

Common mistakes

What students write Priya: 6 cm² × 5 = 30 m² (k applied to area).

The fix Find sides first: 15 m × 10 m; area = 150 m².

Try this Priya says the actual area of a 3 cm × 2 cm drawing at scale 1 cm = 5 m is 30 m² because 6 cm² × 5 = 30 m². Find her error and correct it.

What students write Marcus: 6 ÷ 4 = 1.5 m (divided instead of ×).

The fix Multiply: 6 × 4 = 24 m. drawing × scale = actual.

Try this Marcus finds the actual length of a 6 cm drawing at scale 1 cm = 4 m by computing 6 ÷ 4 = 1.5 m. Find his error and correct it.

Teacher tip

Head off the two predictable errors before they happen. First: Find sides first: 15 m × 10 m; area = 150 m². Second: Multiply: 6 × 4 = 24 m. drawing × scale = actual.