Ajay's father asks him to find the area covered by the grass in his garden. Ajay is informed that the shape of the area covered by the grass is square which has a diagonal length of $16 \sqrt{2}$ meters. What is the area calculated by Ajay is ___ $m^{2}$ .

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Solution

Since area of a square has to be calculated, whose diagonal length is $16 \sqrt{2}$ meters. The relation between diagonal and side of a square is :

$a \sqrt{2} = d$ , where, a = side of the square and d = length of diagonal (from Pythagorean theorem)

$\Rightarrow a \sqrt{2} = 16 \sqrt{2}$

$\Rightarrow$ a=16m.

Therefore, area is given by:

A = $a^{2}$

$\Rightarrow A = 16^{2} = 256 m^{2}$ .

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Ajay's father asks him to find the area covered by the grass in his garden. Ajay is informed that the shape of the area covered by the grass is square which has a diagonal length of 16√2 meters. What is the area calculated by Ajay is ___ m2.

Ajay's father asks him to find the area covered by the grass in his garden. Ajay is informed that the shape of the area covered by the grass is square which has a diagonal length of $16 \sqrt{2}$ meters. What is the area calculated by Ajay is ___ $m^{2}$ .