Geometry and TrigonometryVery hardArea of a stadium shape
Geometry and Trigonometry practice question
A running track's infield consists of a rectangle 100 metres long and 60 metres wide with a semicircle attached to each of the two 60-metre sides. What is the total area of the infield, in square metres?
- A. 6,000 + 900πCorrect
- B. 6,000 + 1,800π
- C. 6,000 + 3,600π
- D. 6,000 + 60π
Answer: A. 6,000 + 900π
Rectangle: 100 × 60 = 6,000. The two semicircles together make one full circle of diameter 60, so radius 30: π(30²) = 900π. Total: 6,000 + 900π.
Why the other answers are wrong
- B. 6,000 + 1,800π
- 1,800π counts two FULL circles; the two semicircles make just one.
- C. 6,000 + 3,600π
- 3,600π uses the diameter, 60, as the radius. The radius is 30.
- D. 6,000 + 60π
- 60π is the circle's CIRCUMFERENCE (2π × 30), not its area.
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