Question

(SAT Prep) The diagonals

BF
and
CE
divide the hexagon ABCDEF into two equilateral triangles and a square. Find the perimeter of the hexagon if BF = 3 cm.

Answer 1

The perimeter would be 18.

Look at the attached sample figure. Since the interior is to be a square, we know that BC=CE=EF=FB. We know that BF=3, so the other sides, BC, CE and EF must be 3 as well.

We know that the two triangles formed are equilateral; thus CD=DE=EC. We know from earlier that EC=3; therefore CD=3 and DE=3.

We have a similar situation with the other triangle. AB=BF=FA; we know that BF=3, so AB=3 and FA=3.

This means all 6 sides are 3, so the perimeter would be 6(3)=18 cm.