Geometry
Perimeter & Circumference
Perimeter is the total distance around a polygon. Circumference is the distance around a circle: C = 2πr or C = πd.
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Find the perimeter of a rectangle with length 8 and width 5
Step-by-Step Solution
P = 2l + 2w
P = 2(8) + 2(5) = 16 + 10 = 26
Answer
P = 26 units
Problem
Find the circumference of a circle with radius 7
Step-by-Step Solution
C = 2πr
C = 2π(7) = 14π ≈ 43.98 units
Answer
C = 14π ≈ 43.98 units
Problem
Find the perimeter of a triangle with sides 5, 12, and 13
Step-by-Step Solution
P = sum of all sides
P = 5 + 12 + 13 = 30
Answer
P = 30 units
Problem
Find the circumference of a circle with diameter 14
Step-by-Step Solution
C = πd
C = π × 14 = 14π ≈ 43.98 units
Answer
C = 14π ≈ 43.98 units
Problem
A square has a perimeter of 36. What is the side length?
Step-by-Step Solution
P = 4s → 36 = 4s
s = 36 ÷ 4 = 9
Answer
Side = 9 units
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Perimeter of a square with side 9?
Circumference of a circle with diameter 10?
Perimeter of rectangle: length 12, width 4?
Circumference of circle with radius 3?
Perimeter of triangle with sides 7, 7, and 10?
Perimeter of a regular hexagon with side 5?
Circumference of circle with radius 7?
Perimeter of rectangle: length 20, width 8?
A square has perimeter 48. What is the side length?
Circumference of circle with diameter 1?
Perimeter of triangle with sides 9, 12, and 15?
A rectangle has perimeter 30 and length 10. What is the width?
Finished all 12? Give yourself a pat on the back — then check your work!
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