Question

Which has greater area, a square of side $42$ m or a rectangle with sides $51$ m and $35$ m and by how much?

Answer 1

Step 1: Finding the area of square.

Give: Side of square $=42\mathrm{m}$

Area of a square $={\left(\text{side}\right)}^2$

$$\begin{gathered} ={\left(42\right)}^2 \\ =1764{\mathrm{m}}^2 \end{gathered}$$

Step 2 : Finding the area of rectangle.

Given length of rectangle$=51\mathrm{m}$ and Breadth $=35\mathrm{m}$

Area of a rectangle $=$ length $\times$breadth

$$\begin{gathered} =51\times 35 \\ =1785{\text{m}}^2 \end{gathered}$$

Step 3: Find the difference of area of Square and Rectangle

Since, $1785{\text{m}}^2{\text{> 1764 m}}^2$

$\Rightarrow$Area of Rectangle > Area of Square

Difference of area $=1785-1764$

${\text{=21 m}}^2$

Hence, Area of rectangle is greater than area of square by $21{\mathrm{m}}^2$.