Question

A side of a regular polygon is 3.5 cm in length. The perimeter of the polygon is 17.5 cm. How many sides does the polygon have?

Answer 1

Hint: As we have the length of a regular polygon = 3.5 cm. The perimeter of the polygon = 17.5 cm. Since we know that the perimeter is the sum of all the sides of a polygon. So, we need to divide the perimeter by the given side to get the number of sides of the given polygon.

Complete step-by-step solution:
As it is given that, the polygon is regular. Therefore, the length of each side of the polygon is 3.5 cm.
Also, we know that the perimeter of the polygon is the sum of all the sides.
So, for a regular polygon of side a, we can have:
$P=n\times a$, where n is the number of sides.
So, for the given polygon, we can have:
$\begin{array}{rl}& \Rightarrow 17.5=n\times 3.5\\ & \Rightarrow n={\displaystyle \frac{17.5}{3.5}}\\ & \Rightarrow n=5\end{array}$
Therefore, we get n = 5
So, the regular polygon has 5 sides.

Hence, we can say that the polygon is a regular pentagon.

Note: The method to find the number of sides using the perimeter and given length of the side by the formula: $P=n\times a$ is only valid for regular polygon, i.e. the polygons with all sides equal such as square, hexagon, regular pentagon, etc. In the case of irregular polygons, say rectangle or any quadrilateral with no side equal, we cannot use this formula. We need some other data to form equations and solve for the number of sides.