GRE Sample Test 5 Quantitative Reasoning 1

Since triangle ABC is inscribed in a semicircle, it must be a right triangle. The area of the triangle is thus $\frac{1}{2}$ 10 × 24 = 120. Using the Pythagorean Theorem, the diameter of the circle = AC = 26. The area of the circle is thus $\left(\mathit{\pi }\right){\mathit{r}}^2$ = $\left(\mathit{\pi }\right){13}^2$ = (π)169. The area of the semicircle is thus $\frac{169\mathit{\pi }}{2}$ = 84.5π. The area of the shaded region = area of the semicircle − area of the triangle. This can be expressed as 84.5π − 120.