# Math Help - Contest problem 5

1. ## Contest problem 5

The game Hexagon consists of some pieces, each in a shape of a regular hexagon with the area 6. Each piece is divided by lines into four right triangles, six isosceles triangles and one quadrilateral (see the picture). What is the area of the shaded quadrilateral?

2. ## Re: Contest problem 5

Originally Posted by Kanwar245
The game Hexagon consists of some pieces, each in a shape of a regular hexagon with the area 6. Each piece is divided by lines into four right triangles, six isosceles triangles and one quadrilateral (see the picture). What is the area of the shaded quadrilateral?
$A_H=\frac{3}{2}a^2 \sqrt 3 \Rightarrow 6=\frac{3}{2}a^2 \sqrt 3 \Rightarrow a^2 \sqrt 3=4 \Rightarrow a^2=\frac{4}{\sqrt 3}$

$A_Q=2\left(\frac{a\cdot a \sqrt 3}{8}\right)=\frac{a^2 \sqrt 3}{4}=1$