Problem Solving

Anurag@Gurome wrote:

sanju09 wrote:When two congruent equilateral triangles share a common center, then their union can be a star as shown. If their overlap is a regular hexagon of area 60, then what is the area of one of the original equilateral triangles?
(A) 10
(B) 15
(C) 30
(D) 60
(E) 90

Easiest Solution:
Area of any of the original triangle must be greater than the overlapping region. Only such option is 90, i.e. option E.

Methodical Tricky Solution:
Join the center of the triangles (also of the hexagon) with the vertices of the hexagon. This will result 6 small equilateral triangles inside the hexagon, each of equal are as shown in the following figure.



Now, each of these six small equilateral triangles are congruent to each of the six equilateral triangles outside the hexagon.

Now, area of hexagon = 6*(Area of an small equilateral triangle) = 60
=> Area of an small equilateral triangle = 60/6 = 10

Area of one of the original equilateral triangle = 9*(Area of an equilateral small triangle) = 90

Correct answer is E.