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
- Happytwin
~savannahsolver