Question

A regular pentagon of each side $12cm$ has same perimeter as that of a regular hexagon. Find the length of each side of the hexagon.

Answer 1

Calculating the perimeter of the regular pentagon

Given,
Side of the regular pentagon $=12cm$
A regular pentagon and a regular hexagon have equal perimeters.

The perimeter of the regular pentagon is given by:
$P=5\left(Side\right)$
$P=5\left(12\right)$
$P=60cm$

Calculating the length of the side of the regular hexagon

Since the perimeter of the regular pentagon and regular hexagon is equal.
Thus,
The perimeter of the regular hexagon
$=$ the perimeter of the regular pentagon
$=60cm$

The perimeter of the hexagon is given by:
$P=6\left(Side\right)$
$60=6\left(side\right)$
$Side=\frac{60}{6}=10cm$

Therefore, the length of the side of the regular hexagon is $10cm$.