# 2005 AMC 10A Problems/Problem 12

## Problem

The figure shown is called a *trefoil* and is constructed by drawing circular sectors about the sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length ?

## Solution

The area of the *trefoil* is equal to the area of a small equilateral triangle plus the area of four sectors with a radius of minus the area of a small equilateral triangle.

This is equivalent to the area of four sectors with a radius of .

So the answer is:

## See Also

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.