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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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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