Find the area and the perimeter of a regular | vedclass

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Question

(D) regular hexagon consists of $6$ equilateral triangles with side length $a = 12\,cm$.Perimeter of a regular hexagon $= 6 	imes a = 6 	imes 12\,cm

Vedclass · Accepted Answer

$72\,cm$,$216\sqrt{3}\,cm^2$

Vedclass · Answer

(D) regular hexagon consists of $6$ equilateral triangles with side length $a = 12\,cm$.Perimeter of a regular hexagon $= 6 	imes a = 6 	imes 12\,cm = 72\,cm$.Area of one equilateral triangle $= \frac{\sqrt{3}}{4} 	imes a^2 = \frac{\sqrt{3}}{4} 	imes 12^2 = \frac{\sqrt{3}}{4} 	imes 144 = 36\sqrt{3}\,cm^2$.Total area of the hexagon $= 6 	imes 36\sqrt{3}\,cm^2 = 216\sqrt{3}\,cm^2$.Thus,the perimeter is $72\,cm$ and the area is $216\sqrt{3}\,cm^2$.

Find the area and the perimeter of a regular hexagon having length of each side $12\,cm$.

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