SME
Grade 3 Math · Problem type
Same area, different perimeter
Use this for rectangles with the same area but different perimeters.
Diagram
This is an example. Type your own values to start a new problem.
Length (cm)
×
Width (cm)
=
Area (cm²)
Perimeter
calculated
Formulas
6 + 4 + 6 + 4 = 20
Length + width + length + width = perimeter
6 × 4 = 24
Length × width = area
Assumptions
•
Rectangles with the same area can have different perimeters.
•
A long thin rectangle has a bigger perimeter than a square one.
•
Keep the area and change the length to compare.
Step-by-step
WE KNOW
Area: 24 cm²
Length: 6 cm
FIND
width, perimeter
Step 1 · Find width
6 × ? = 24
Length × width = area
Divide the area by the length.
Width = 24 ÷ 6
Think: 6 × ? = 24
Double 6: 6 + 6 = 12
Double again: 12 + 12 = 24
4 groups of 6 make 24
Width = 4 cm
Step 2 · Find perimeter
6 + 4 + 6 + 4 = ?
Length + width + length + width = perimeter
Add all four sides.
6 + 4 = 10
10 + 6 = 16
16 + 4 = 20
Perimeter = 20 cm
Check
Put the numbers back in. Both sides should match.
6 + 4 + 6 + 4 = 20 ✓
6 × 4 = 24 ✓
Topic check
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