Question 46

An equilateral triangle, having each side as a , has its corners cut away so as to form a regular hexagon. The area of the hexagon is

Solution

To make a regular hexagon, three equilateral triangles of side$$\ \frac{\ a}{3}$$ will be cut from the corners to make a regular hexagon of side a.

Hence, this hexagonal can be further divided into 6 equilateral triangles of side $$\ \frac{\ a}{3}$$.

Hence the area of the hexagon = $$\ 6\cdot\ \frac{\ \sqrt{\ 3}}{4}$$*($$\ \ \frac{\ a}{3}$$)$$^2$$ = $$\frac{\sqrt3 a^2}{6}$$

A is the answer.

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