SME
Grade 7 Math · Problem type
Scale factor and area
Use this for “A triangle with base 4 and height 3 is copied at scale factor 2. What is the copy’s area?”
Diagram
Scale factor 2: every length times 2
Width: 4 × 2 = 8
Height: 3 × 2 = 6
Area: 6 × 2 × 2 = 24
This is an example. Type your own values to start a new problem.
A
=
w
×
h
÷
2
B
=
A
×
k
×
k
Formulas
A
=
w
×
h
÷
2
(area
=
base
×
height
÷
2)
6 = 4 × 3 ÷ 2
B
=
A
×
k
×
k
(copy
area
=
area
×
scale
factor
×
scale
factor)
24 = 6 × 2 × 2
Assumptions
•
Every length of the copy is k times the original’s.
•
The copy is k times as wide and k times as tall: k × k times the area.
•
A scale factor of 3 makes 9 times the area, not 3 times.
Step-by-step
WE KNOW
k = 2 (scale factor), w = 4 (base), h = 3 (height)
FIND
area (A), copy area (B)
Step 1 · Find area (A)
Use A = w × h ÷ 2 (area = base × height ÷ 2)
A triangle is half of its base times its height.
A
=
4
×
3
2
A
=
12
2
A
=
6
Step 2 · Find copy area (B)
Use B = A × k × k (copy area = area × scale factor × scale factor)
The
copy
is
k
times
as
wide
and
k
times
as
tall:
k
×
k
times
the
area.
B
=
6
×
2
×
2
B
=
12
×
2
B
=
24
Check
Put the numbers back in. Both sides should match.
6 = 4 × 3 ÷ 2 ✓
24 = 6 × 2 × 2 ✓
Topic check
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