# Difference between revisions of "2005 AMC 10A Problems/Problem 12"

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## Revision as of 21:46, 3 August 2006

## 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 equivilant to the area of four sectors with a radius of .

So the answer is: