Which of the following figures has the same shaded area as that of the given circle?
Correct answer: C. A triangle with a base equal to the circle's diameter and height equal to the radius
- A. A square with side length equal to the diameter of the circle
- B. A rectangle with length equal to the diameter of the circle and width equal to half the radius
- C. A triangle with a base equal to the circle's diameter and height equal to the radius
- D. A parallelogram with base equal to the circle's diameter and height equal to the radius
Explanation
The correct answer is the triangle with a base equal to the circle's diameter and height equal to the radius. The area of the circle is πr², while the area of the triangle is 1/2 × base × height = 1/2 × 2r × r = r². Thus, these areas are equivalent when π is approximated to 3. Option A (square) and Option B (rectangle) do not match the circle's area, while Option D (parallelogram) also does not have the same area as the circle.
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