Question

How do you find the perimeter and area of a square of side $6\dfrac{1}{2}$ units?

Answer 1

Here the length of the side of the square is given in mixed number form and converted to fractional number or decimal number, in order to perform algebraic calculations with it. We can calculate the area of a square as ${a^2}$, where a is the side of the square. Perimeter of a square is given as $4 \times a$, where a is again the side of the square.

Complete step by step solution:
In this question, side of the square is given in mixed fraction we have to
convert it into fraction,

So converting $6\dfrac{1}{2}$ into fractional form,
$\Rightarrow 6\dfrac{1}{2} = \dfrac{{6 \times 2 + 1}}{2} = \dfrac{{12 + 1}}{2} = \dfrac{{13}}{2}$

So, we got the value of the side of the square converted into fractional form.
Now we know that the perimeter of a square of side $a$ is given as $4 \times a$

Therefore, perimeter of the square $= 4 \times a = 4 \times \dfrac{{13}}{2} = 26$ units
Now in order to find the area, we know that area of a square is given as ${a^2}$, where a is the side of the square.

Therefore, area of the square $= {a^2} = {(\dfrac{{13}}{2})^2} = \dfrac{{{{13}^2}}}{{{2^2}}} = \dfrac{{169}}{4}$ units square

So we got the area $= \dfrac{{169}}{4}$ units square, but this is in an improper fraction form, so we
have to convert it into mixed form by following
$169 \div 4 = 42$ as whole number and $1$ as remainder
$\therefore$ required mixed form $= 42\dfrac{1}{4}$

i.e. perimeter and area of the square $= 26{\text{unit}}\;{\text{and}}\;42\dfrac{1}{4}{\text{uni}}{{\text{t}}^2}$ respectively.

Note: Do write the units of the parameters and quantities. Students generally get confused between $\dfrac{{a \times c + b}}{c}\;{\text{and}}\;\dfrac{{a \times b + c}}{c}$ for conversion of mixed fraction $a\dfrac{b}{c}$ to fraction, keep in mind that $\dfrac{{a \times c + b}}{c}$ is the correct formula for conversion.