In the figure above, squares PQRV and VRST have sides of length 6 cm.Quantity A: The area of the shaded region PQS.Quantity B: 36cm2
Correct answer: C. The two quantities are equal.
- A. Quantity A is greater.
- B. Quantity B is greater.
- C. The two quantities are equal.
- D. The relationship cannot be determined from the information given.
Explanation
To find the area of the shaded region PQS, note that PQS forms a right triangle with base PQ and height QS. Since squares PQRV and VRST have sides of 6 cm, the diagonal PQ (or QS) is 6√2 cm, but for the triangle's area calculation, we consider the base and height along the sides of the square. The area of triangle PQS is 1/2 * base * height = 1/2 * 12 * 6 = 36 cm2, which equals Quantity B. Therefore, Quantity A and Quantity B are equal.
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