Find the area and perimeter of a square plot of land whose diagonal is 24 m long.

Solution:

Area of the square $=\frac{1}{2} \times$ Diagonal $^{2}$

$=\frac{1}{2} \times 24 \times 24$

$=288 \mathrm{~m}^{2}$

Now, let the side of the square be x m.
Thus, we have:

Area $=$ Side $^{2}$

$\Rightarrow 288=x^{2}$

$\Rightarrow x=12 \sqrt{2}$

 

$\Rightarrow x=16.92$

Perimeter $=4 \times$ Side

$=4 \times 16.92$

 

$=67.68 \mathrm{~m}$

Thus, the perimeter of the square plot is 67.68 m.