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?
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.
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.