# 2017 AMC 8 Problems/Problem 25

## Problem

In the figure shown, and are line segments each of length 2, and . Arcs and are each one-sixth of a circle with radius 2. What is the area of the region shown?

## Solution 2

In addition to the given diagram, we can draw lines and The area of rhombus is half the product of its diagonals, which is . However, we have to subtract off the circular segments. The area of those can be found by computing the area of the circle with radius 2, multiplying it by , then finally subtracting the area of an equilateral triangle with a side length 2 from the sector. The sum of the areas of the circular segments is The area of rhombus minus the circular segments is

~PEKKA

## Video Solutions

~savannahsolver