Question

A side of a regular hexagon measures 5 cm. What is the length of a side of a regular pentagon with the same perimeter?

• A. 5 cm
• B. 12 cm
• C. 9 cm
• D. 6 cm

Answer 1

The correct option is D 6 cm

Length of a side of the given hexagon
= 5 cm

A regular polygon has all sides equal.

$⟹$ Each of the 6 sides of the regular hexagon measures 5 cm.

$⟹$ Perimeter of the regular hexagon
= 5 cm + 5 cm + 5 cm + 5 cm +
5 cm + 5 cm
= 30 cm

It is given that the regular pentagon has a perimeter of 30 cm.

Let the length of a side of the regular pentagon be $x$ cm.

Since the pentagon is regular, each of the 5 sides measures $x$ cm.

$\Rightarrow$ Perimeter of the regular pentagon
$=5\times x=5x\text{cm}$

$⟹5x=30$

$⟹x=\frac{30}{5}=6$ cm

Thus, each side of the regular pentagon measures 6 cm.