Question

The perimeter of a regular polygon is 164.5cm and length of each side is 23.5cm .Find the number of sides of this polygon . What name it has ?

Answer 1

Answer: 7

Step-by-step explanation:

Perimeter of a regular polygon= 164.5 cm

Length of each side= 23.5 cm

Hence, no. of sides= (164.5 ÷ 23.5) = 7

The polygon has 7 sides.

The name of the polygon is heptagon.

Answer 2

Answer:

  The total number of side the polygon has is 7. Therefore, the polygon is called heptagon ( regular heptagon ).

Step-by-step explanation:

Given -

The perimeter of the regular polygon =  164.5 cm

Measure of the each side of the polygon = 23.5cm

To find -  The number of sides

A polygon whose all the sides and angles are equal is called regular polygon.

The perimeter of the regular polygon = 164.5 cm ( Given )

Now,

Sum of total no. of sides of the polygon =  164.5 cm ( Perimeter of a polygon is equal to the sum of all the sides of a polygon.)

Let the total number of sides of this unknown polygon be x

This implies,

Sum of total no. of sides of the polygon =  164.5 cm

23.5cm + 23.5cm + 23.5cm + 23.5cm+..... (x times)  = 164.5 cm ( Given that side of regular polygon is 23.5cm)

(23.5 cm)x = 164.5cm

x =  164.5cm / 23.5 cm

x = 7.

Thus,

there are 7 sides for this regular polygon which makes it a regular heptagon.

Thank you.