SSAT Math Question 309: Answer and Explanation

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Question: 309

3. A circle is inscribed in a square with a side length of 12. Find the area of the shaded region.

A. 144
B. 36π
C. 12π
D. 144 – 36π

Correct Answer: D

Explanation:

The answer is D

Questions seeking the area of a weird shaded region generally require you to subtract the area of one normal shape from the area of another normal shape. In this case, subtract the area of the circle from the area of the square. The area of a square is s², in this case 12² = 144. The area of the circle is πr². If you draw in a diameter, you will see that the diameter is the same length as the side of the square, so the radius is 6. Thus, the area of the circle is π(6)² = 36π. Choice (D) reflects the difference between the two areas.

You can estimate that the area is a tiny fraction of the area of the square (144). Estimate the values of the answer choices, replacing π with 3 to keep the math simple. Choice (D) is a reasonable estimate. The other choices are too big or, in the case of choice (E), less than zero.

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