Question

How do you find the area of a square whose perimeter is $52$ cm?

Answer 1

Hint:First of all, consider the length of side of the given square to be something constant (any alphabet), then with help of it write the perimeter equation for the square and solve that to get the length of the square. Finally with the help of the formula for area of a square find the required area.Perimeter of a square of side “a” is given as, $P = 4 \times a$. And the area of a square of side “a” is given as, $A = a \times a = {a^2}$.

Complete step by step answer:
In order to find the area of the given square whose perimeter is $52$ cm, let us consider first the length of sides of the square to be $x$.Now it is given that its perimeter is $52$ cm, so we can write it as
$4 \times x = 52$
Dividing both sides with $4$ to get length of the sides,
$\dfrac{{4 \times x}}{4} = \dfrac{{52}}{4} \\
\Rightarrow x = 13$
So we get the length of side $ = 13$ cm.Now we know that area of a square with side “a” is given as,
$A = a \times a = {a^2}$
Substituting the value of length of side in the area formula, we will get
$A = 13 \times 13 = 169$

Therefore the required area of the given square is equals to $169\;{\text{c}}{{\text{m}}^2}$.

Note: When writing the physical quantities like perimeter, area or volume then must write their units together, not writing the units will cause in deducing your marks. Also, when solving objective type questions check the unit of quantities in the question and answer if they are the same or not, if not the same then reduce them into the same ones.