Problem:
The twelve-sided figure shown has been drawn on graph paper. What is the area of the figure in
Answer Choices:
A.
B.
C.
D.
E.
Solution:
To solve for the area of the figure, we seperate the compound shape into parts that are easier to work with, as such:
As is now clear, there is the center square (in pink), with smaller triangles surrounding it (in blue). The area of the square is
The other triangles each have a base of and a height of , so their area is equal to
There are of these triangles, so their total area is
Therefore, the total area is
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions