Corners are cut off from an equilateral triangle T to produce a regular hexagon H. What is the ratio of the area of H to the area of T?
+357 Drawing it out would help, but I'm new to the "write code to make funny pictures on web2.0.calc" thing so this is the best I can do.
The side of the triangle is ABC = 3a
The side of the hexagon = a
Area of triangle = (root3 /4 )*(3a)^2 = 9a^2 *(root3/4)
Area of hexagon with side a = 6*(root3 /4 )*(a)^2
Ratio of areas of hexagon to that of triangle = { 6*(root3 /4 )*(a)^2 } / { 9a^2 *(root3/4)} = 6/9 = 2/3
and we get = 2 : 3
Yay!
