2008 AMC 10A Problem 17

Problem 17 of 25IntermediateGeometry

An equilateral triangle has side length

6.

What is the area of the region containing all points that are outside the triangle and not more than

3

units from a point of the triangle?

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Solution

Along each of the three sides is a

6 \times 3

rectangle, contributing

3 \cdot 6 \cdot 3 = 54.

At each vertex is a

120^\circ

sector of radius

3;

the three together form a full circle of area

\pi \cdot 3^2 = 9\pi.

The total area is

54 + 9\pi.

Thus, the correct answer is B.