Question

What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides.

Answer 1

Hint: We know that a polygon is a closed 2-D figure made of a finite number of straight line segments and regular polygon means that all sides and interior angles are equal. On the basis of side we named a regular polygon.

Complete step-by-step solution
A regular polygon is a polygon having the properties follows:
(1) The measures of its interior angles are equal.
(2) The length of its sides are equal.
On the basis of number of side the given regular polygon named as follows:
(i) 3 sides
A regular polygon having 3 sides is known as an equilateral triangle. Each interior angle is equal to $60{}^\circ $.

(ii) 4 sides
A regular polygon having 4 sides is known as square. Each interior angle is equal to $90{}^\circ $.

(iii) 6 sides
A regular polygon having 6 sides is known as a regular hexagon and its interior angle is equal to $120{}^\circ $.

Note: Remember all the names according to the number of sides of a regular polygon.
Also, remember that each interior angle of any regular polygon having ‘n’ sides is given by,
$\theta =\left( \dfrac{n-2}{n} \right)\times 180{}^\circ $
The students might just write the answer as triangle and quadrilateral, but here we have been given that we have to name regular polygons, so students have to take care of this mistake.