SOLUTION: In the figure above, two identical equilateral triangles, JKL and XYZ, intersect so that and the six small triangles formed are identical. If the area of the regular hexagon forme

Algebra ->  Circles -> SOLUTION: In the figure above, two identical equilateral triangles, JKL and XYZ, intersect so that and the six small triangles formed are identical. If the area of the regular hexagon forme      Log On


   

Question 955402: In the figure above, two identical equilateral triangles, JKL and XYZ, intersect so that and the six small triangles formed are identical. If the area of the regular hexagon formed by the intersection of the triangles is 60 square units, what is the area, in square units, of the entire figure?
IMAGE: http://jasper.kaptest.com/content/media/64/124564.9.3905a322-f66a-4e3e-86ee-5f59669cf669.png
OPTIONS:
80
90
100
120
160
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
a=side of hexagon=side of triangle(star points); A=Area of hexagon=60
a=3%5E%281%2F4%29sqrt%282%28A%2F9%29%29=1.32%28sqrt%2813.33%29%29=1.32%283.65%29=4.82
Sides of the hexagon (and triangles) measure 4.82 units.
For the triangles:
Area=%281%2F4%29sqrt%283%29a%5E2=1%2F4sqrt%283%29%284.82%29%5E2=0.4330%2823.23%29=10.06units%5E2
There are 6 triangles=6(10.06)=60.36 sq units
Hexagon+triangles=60 sq units+60 sq units=120 sq units
---OR---
The triangles folded in have same area as the hexagon, so total area=2(60 sq units)=120 sq units.
ANSWER: Total area is 120 square units.