Question

Mahesh is making a paper mobile. He draws and cuts out a square with sides 4.5cm long. Next he draws a regular hexagon with the same perimeter as the square. How long is each side of the regular hexagon?
Perimeter = distance around a figure

A.3cm
B.6cm
C.18cm
D.27cm

Answer 1

Hint: The boundary of a geometrical figure formed by a continuous line is called its perimeter. The value of the perimeter is the length of this boundary. Different figures have different formulas for calculating their perimeter; it is simply the sum of all the sides present in the figure. As the perimeter of the square and hexagon are equal, compare their formulas to find out the measure of each side of the hexagon.

Complete step-by-step answer:
As the perimeter is the sum of all the sides in a figure, the square has four sides so its $ perimeter = side + side + side + side = 4 \times side $ .
A hexagon has six sides so its $ perimeter = side + side + side + side + side + side = 6 \times side $ .
We are given that the hexagon is regular, that's why we take the length of all its sides equal.
The perimeter of the square with side 4.5cm, $ {P_1} = 4 \times 4.5cm = 18cm $
As the perimeter of the square is the same as the perimeter of the hexagon so,
 $
  {P_2} = 18cm \\
  6 \times side = 18\;cm \\
   \Rightarrow side = 3\;cm \;
  $
Thus, each side of the regular hexagon is 3 cm long.
So, the correct answer is “Option A”.

Note: Two figures having the same perimeter signify that when both of them are cut at one point and stretched out as a straight wire, both the wires would have the same length.