Question

Find the area of a regular hexagon if the area of equilateral triangle inside it 24sq cm.

Answer 1

Answer:

The correct answer for the given regular hexagon will be $144cm^{2}$.

Step-by-step explanation:

We know that the regular hexagon is made of six equal sides and when each vertex is joined to the center point of the hexagon, each of the six triangles formed are equilateral. As the hexagon is made up of six identical equilateral triangles, the area of the regular hexagon ($A_{h}$) will be:

$A_{h}=6$×$A_{t}$

We are given that the area of the equilateral triangle ($A_{t}$) is $24cm^{2}$, so:

$A_{h}=6(24) cm^{2}$

$A_{h}=144cm^{2}$

Thus, the area of the given regular hexagon is found to be $144cm^{2}$.