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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? Aug 9, 2017

#1
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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.

Aug 9, 2017

#1
+3

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.

hectictar Aug 9, 2017
#2
+1

Call the side of a square, s......and call a side of a triangle, t

So

9s + 2t  = 127

And

s + 2t  = 55    subtract the second equation from the first

8s  = 72        divide both sides by 8

s  = 9

So...the area of any of the squares  = s^2  = 9^2  = 81 sq units   Aug 9, 2017