Geometry and TrigonometryVery hardCircle matched to a square's perimeter
Geometry and Trigonometry practice question
A circle's circumference is equal to the perimeter of a square with side length π. What is the area of the circle?
- A. 4πCorrect
- B. π²
- C. 16π
- D. 2π
Answer: A. 4π
The square's perimeter is 4π, so the circle's circumference 2πr = 4π, giving r = 2. Area = π(2²) = 4π.
Why the other answers are wrong
- B. π²
- π² is the AREA of the square, not the circle.
- C. 16π
- 16π uses r = 4, the perimeter with the π stripped off; but 2πr = 4π gives r = 2.
- D. 2π
- 2π is the circumference of a circle of radius 1, or r × π with r = 2 — not the area.
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