2008 AMC 10A Problems/Problem 17

From AoPSWiki

Problem

An equilateral triangle has side length $6$ . What is the area of the region containing all points that are outside the triangle but not more than $3$ units from a point of the triangle?

$\mathrm{(A)}\ 36+24\sqrt{3}\qquad\mathrm{(B)}\ 54+9\pi\qquad\mathrm{(C)}\ 54+18\sqrt{3}+6\pi\qquad\mathrm{(D)}\ \left(2\sqrt{...$

Solution

pointpen = black; pathpen = black+linewidth(0.7); pen d = linetype("6 6")+linewidth(0.7);pair A=(0,0),B=(6,0),C=6*e...

The region described contains three rectangles of dimensions $3 \times 6$ , and three $120^{\circ}$ degree arcs of circles of radius $3$ . Thus the answer is $3(3 \times 6) + 3 \left( \frac{120^{\circ}}{360^{\circ}} \times 3^2 \pi\right) = 54 + 9\pi \Longrightarrow \mathrm{(B)}.$

2008 AMC 10A (Problems • Resources)
Preceded by Problem 16	Followed by Problem 18
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

Personal tools

Navigation

Search

Toolbox

2008 AMC 10A Problems/Problem 17

From AoPSWiki

Problem

Solution

See also