Question

In the figure below, DOG, ION, and IDO are congruent and isosceles, each with perimeter 55. The quadrilaterals FLIN, DIES, and DRAG are all squares. The perimeter of the 11-sided polygon DRAGONFLIES is 127.

What is the area of DRAG?

Answer 1

Let's call the sides that are length  DG " s " .

And let's call the sides that are length  GO  " t ".

Since the perimeter of each triangle is 55...

s + t + t  =  55

s + 2t  =  55

2t  =  55 - s

Since the perimeter of the entire figure is 127...

9s + 2t  =  127            

Since  2t = 55 - s  ,  we can replace  2t  with  55 - s .

9s + (55 - s)  =  127

8s + 55  =  127             Subtract  55  from both sides.

8s  =  72                       Divide both sides by  8  .

s  =  9

And...the area of the square DRAG  =  DG2  =  s2  =  92  =  81 sq. units.