Question

The figure shows an irregular quadrilateral and the lengths of its individual sides. Which of the following equations best represents the perimeter of the quadrilateral?

A. \[{\text{4}}{{\text{m}}^{\text{2}}}{\text{ + 5}}\]
B. \[{\text{5m + 5}}\]
C. \[{\text{2}}{{\text{m}}^{\text{4}}}{\text{ + 5}}\]
D. \[{{\text{m}}^{\text{4}}}{\text{ + 5}}\]

Answer 1

Hint: Perimeter of a polygon stands for the length of the sum of all the sides of the polygon. So to find the perimeter we have to add the lengths of the sides. In this case, the polygon is a quadrilateral.

Complete step by step solution: Now, a quadrilateral has 4 sides. So to find the perimeter we need to calculate the sum of lengths of the 4 sides.
Length of the 1st Side \[{\text{ = m + 3}}\]
Length of the 2nd Side \[{\text{ = m}}\]
Length of the 3rd Side \[{\text{ = 2m}}\]
Length of the 4th Side \[{\text{ = m + 2}}\]

So, now the length of the perimeter of the quadrilateral is,
\[{\text{ = (m + 3) + m + 2m + (m + 2)}}\]
On addition, we get,
\[{\text{ = 5m + 5}}\]
So, we have the perimeter as \[{\text{5m + 5}}\]

Hence, the correct option is (B)

Note: If opposite sides are equal, then we have the perimeter as, $2\times{({\text{Side}}_1+{\text{Side}}_2)}$. And if all are equal then, the perimeter is $4\times{(1^{\text{st}}\:\text{Side}})$. The same question can be asked in many ways. for example, Himanshu ran 4 rounds of the ground of the above shape. how much he ran. Ultimately, we need to find the perimeter.