The following practice questions ask you to calculate shaded areas involving circles, squares, and triangles. Be careful, though: one of the questions may be a trap.

## Practice questions

**A square is inscribed within a circle.**If it has a side length of what is the area of the shaded portion of the drawing?- What is the area of the shaded triangle?
**A.**54**B.**42**C.**27**D.**21

## Answers and explanations

**The correct answer is Choice (B).**First find the area of the square: For the area of the circle, you need its radius. Cut the square in half, corner to corner, to form two 45-45-90 triangles, where each hypotenuse is the diameter of the circle. If the side of this triangle is the hypotenuse is 2, because in a right triangle, the square of the hypotenuse is the sum of the squares of the other two sides:*c*^{2}= 4, so is the diameter of the circle, and the radius of the circle is half the diameter, or 1. Now for the area of the circle: Subtract the area of the square from the area of the circle for your answer:**The correct answer is Choice (D).**For the area of a triangle, multiply the base by the height and divide by 2. The base of this triangle is 7, and the height is 6, for an area of 21. The 2 in the drawing has no bearing.