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SAT Subject Test

Rectangle is inscribed in the circle shown above. If the length of side is and the length of side is , what is the area of the shaded region?

### Select an Answer

Correct Answer:

No

Correct Answer:

No

Correct Answer:

Yes

Correct Answer:

No

Correct Answer:

No

### View Correct Answer

The correct answer is C.

The area of the shaded region can be found by subtracting the area of rectangle from the area of the circle. To determine the area of the circle, first find the radius , and then compute the area . Since rectangle is inscribed in the circle, is an inscribed right angle, and thus is a diameter of the circle. Applying the Pythagorean theorem to right triangle ,one finds the length of side is Thus the radius of the circle is , and the area of the circle is . The area of rectangle is , and therefore, the area of the shaded region is .

Question Difficulty:

hard