Question

find the area of square field whose one diagonal is 24m

Answer 1

Let side be x
Therefore by Pythagoras theorem,
2x²=diagonal²
2x²=24²
2x²=576
x²=288

Therefore area is 288m

Answer 2

The area of square field is $288m^{2}.$

Step-by-step explanation:

Given,

The diagonal of square field = 24 m

To find, the area of square field = ?

Let the side of square = a m

We know that,

The diagonal of square = $\sqrt{2}$ × Side, a

∴ $\sqrt{2}a=24$

⇒ $a=\dfrac{24}{\sqrt{2}} m$

∴ The area of square field = $a^{2}$

$=(\dfrac{24}{\sqrt{2}})^{2}$

$=\dfrac{24}{\sqrt{2}}\times \dfrac{24}{\sqrt{2}}$

$=\dfrac{576}{2} =288m^{2}$

Hence, the area of square field is $288m^{2}.$