Question

These two trapezoids are similar. If DC = 10 centimeters, SR = 15 centimeters, and the area of ABCD is 72 square centimeters, then the area of PQRS is __________ square centimeters.

a) 27
b) 48
c) 64
d) 96

Answer 1

To find the area of trapezoid PQRS, we can use the fact that the two trapezoids are similar. Using the given information, we can determine the length of PQ and then use the formula for the area of a trapezoid to find the area of PQRS. The provided options do not include the correct answer, so please verify the given information.

Step-by-step explanation:

To find the area of trapezoid PQRS, we can use the fact that the two trapezoids are similar. Since the corresponding sides of similar figures are proportional, we can set up the following ratio:

(PQ/AB) = (SR/CD)

Plugging in the given values, we get (PQ/10) = (15/10). Solving for PQ, we find PQ = 15.

Now, we can use the formula for the area of a trapezoid: (1/2) * (base1 + base2) * height. Plugging in the values, we get (1/2) * (10 + 15) * 15 = 11.25. Therefore, the area of trapezoid PQRS is 11.25 square centimeters. The answer is not one of the provided options, so please check if the question is complete or if there might be a mistake in the given information.