SME
Grade 3 Math · Problem type
Same perimeter, different area
Use this for “Which rectangle has the same perimeter as this one?”
Diagram
This is an example. Type your own values to start a new problem.
Length (cm)
+
Width (cm)
+
Length (cm)
+
Width (cm)
=
Perimeter (cm)
Area
calculated
Formulas
6 + 4 + 6 + 4 = 20
Length + width + length + width = perimeter
6 × 4 = 24
Length × width = area
Assumptions
•
Rectangles with the same perimeter can have different areas.
•
Perimeter goes around the edge. Area covers the inside, in square units.
•
Keep the perimeter and change the length to compare.
Step-by-step
WE KNOW
Length: 6 cm
Perimeter: 20 cm
FIND
width, area
Step 1 · Find width
6 + ? + 6 + ? = 20
Length + width + length + width = perimeter
Take away the two lengths. The two widths share what is left.
20 − 6 − 6 = 8
8 ÷ 2 = 4
Width = 4 cm
Step 2 · Find area
6 × 4 = ?
Length × width = area
Rows of squares: multiply the length by the width.
5 × 4 = 20
One more group: 20 + 4 = 24
Area = 24 cm²
Check
Put the numbers back in. Both sides should match.
6 + 4 + 6 + 4 = 20 ✓
6 × 4 = 24 ✓
Topic check
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