Two hexagons

Geometry Level 2

The $ABCDEF$ hexagon is regular, with an area of $1$ . The $X, Y$ points are the midpoints of the $CD$ and $EF$ sides.

If the area of the $ABCXYF$ hexagon can be expressed as $\dfrac{a}{b}$ , where $a$ and $b$ are coprime integers, then what is the value of $a+b$ ?

2 solutions

Marta Reece
Jul 30, 2017

Divide the hexagon into $24$ equal equilateral triangles as shown.

$19$ of them are red.

The area of the entire hexagon has been given as $1$ .

The red area is therefore $\dfrac{19}{24}$

And the answer is $19+24=\boxed{43}$

Ahmad Saad
Jul 30, 2017