Geometry and TrigonometryVery hardArea between a quarter circle and a triangle
Geometry and Trigonometry practice question
A quarter circle has radius 4, with its two straight edges meeting at the centre O. The chord joining the ends of the arc cuts off a segment of the circle. What is the area of that segment?
- A. 4π − 8Correct
- B. 4π
- C. 8π − 8
- D. 16π − 8
Answer: A. 4π − 8
The quarter circle has area 4π, and the right triangle inside it has area (1/2)(4)(4) = 8, so the segment is 4π − 8.
Why the other answers are wrong
- B. 4π
- 4π is the whole quarter circle.
- C. 8π − 8
- 8π − 8 uses a half circle.
- D. 16π − 8
- 16π − 8 uses the full circle.
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