7th Grade Scale Drawings Worksheet Solutions (PDF)

7th Grade math worksheet solutions: Scale Drawings – Maths PDF

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This scale drawings answers for 7th Grade covers scale drawings (Common Core 7.G.A.1), with a free PDF to print.

Use this answer key to check your work on the scale drawings worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.

Grade 7 · Common Core State Standards: 7.G.A.1

Scale drawings answers: exercises 1 to 10

Exercise 1 – Actual length

$3\times 5=15$

15 feet

3 inches = 15 feet.

Exercise 2 – Map distance

$4.5\times 20=90$

90 miles

Map ratio table.

Exercise 3 – Length on the drawing

$36\div 6=6$

6 inches

Exercise 4 – Scale factor

10 ft = 120 in, so the scale is $2 : 120$.

$2\div 120=1\div 60$

1 : 60

Scale factor 1 : 60.

Exercise 5 – Room dimensions

Length: $3\times 4=12$ ft. Width: $2.5\times 4=10$ ft.

Area: $12\times 10=120$ square feet.

12 ft by 10 ft; 120 square feet

Exercise 6 – Area from a drawing

Each square inch stands for $5\times 5=25$ square feet.

$6\times 25=150$

150 square feet

Area ratio.

Exercise 7 – Fraction scale

Each $\frac{1}{4}$ in is 1 ft, so each inch is 4 ft.

$3\frac{3}{4}\times 4=\frac{15}{4}\times 4=15$

15 feet

Exercise 8 – Find the scale

$20\div 2.5=8$

1 in = 8 ft

Exercise 9 – Enlargement

$8\times\frac{3}{16}=\frac{24}{16}=\frac{3}{2}$

$1\frac{1}{2}$ inches

Exercise 10 – Compare areas

Drawing: $24\div 6=4$ in by $18\div 6=3$ in; area $12$ square inches.

Actual area: $24\times 18=432$ square feet.

$432\div 12=36$

4 in by 3 in; 12 sq in; 36 times as large

Exercises 11 and up

Exercise 11 – Two-leg trip

Total on the map: $1.5+2.25=3.75$ in.

$3.75\times 40=150$

150 miles

Exercise 12 – New scale

Actual length: $4\times 10=40$ ft.

$40\div 5=8$

8 inches

Exercise 13 – Triangle area

Base: $6\times 3=18$ ft. Height: $4\times 3=12$ ft.

$A=\frac{1}{2}(18)(12)=108$

108 square feet

Exercise 14 – New carpet

Actual size: $5\times 3=15$ ft by $3.5\times 3=10.5$ ft.

Area: $15\times 10.5=157.5$ square feet.

Cost: $157.5\times 4.50=708.75$

$708.75

Exercise 15 – Drive time

Distance: $2.75\times 40=110$ miles.

$110\div 55=2$

2 hours

Exercise 16 – Model airplane

40 ft = $40\times 12=480$ in.

$480\div 48=10$

10 inches

The scale 1 : 48.

Exercise 17 – Window on a blueprint

1 in = 2 ft, so $1.5\times 2=3$

3 feet

Exercise 18 – Garden fence

Actual size: $18$ ft by $12$ ft.

Area: $18\times 12=216$ square feet.

Perimeter: $2(18+12)=60$ ft; cost $60\times 2.25=135$

216 square feet; $135

Actual garden.

Exercise 19 – Playground area

Each square inch stands for $15\times 15=225$ square feet.

$12\times 225=2700$

2,700 square feet, so 2,700 tiles

Exercise 20 – Mural plan

Width: $15\div 1.5=10$ in. Height: $9\div 1.5=6$ in.

Area: $10\times 6=60$ square inches.

10 in by 6 in; 60 square inches

The mural plan.

Key facts behind this scale drawings answers

Key facts

The scale is a rate: $1 in = 5 ft$ means 5 feet per 1 inch.
Actual length = drawing length * rate; drawing length = actual length ÷ rate.
Scale factor compares drawing length to actual length in the same units.
Actual area = drawing area * (rate)^2.
To change scales, find actual lengths first, then divide by the new rate.

How to use this scale drawings answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

Download the scale drawings answers as a PDF with the button below and keep it with your notes.

All Grade 7 chapters: Grade 7 math.

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