Question

The diagonal of a square has a length of 10√2. Find the area of the square?

Answer 1

Answer:

Given :

• The diagonal of a square has a length of 10√2.

To Find :-

• What is the area of the square.

Formula Used :-

$\bigstar$ Length Of Diagonal Of Square Formula :

$\mapsto \sf\boxed{\bold{\pink{Length\: of\: Diagonal_{(Square)} =\: a\sqrt{2}}}}$

$\bigstar$ Area Of The Square Formula :

$\mapsto \sf\boxed{\bold{\pink{Area_{(Square)} =\: (a)^2}}}$

where,

• a = Side Of Square

Solution :-

First, we have to find the side of square :

Given :

• Length of diagonal of square = 10√2 cm

According to the question by using the formula we get,

$\implies \sf a\sqrt{2} =\: 10\sqrt{2}$

$\implies \sf a =\: 10\sqrt{2} \times \dfrac{1}{\sqrt{2}}$

$\implies \sf a =\: \dfrac{10\cancel{\sqrt{2}}}{\cancel{\sqrt{2}}}$

$\implies \sf\bold{\purple{a =\: 10\: cm}}$

Now, we have to find the area of the square :

Given :

• Side of Square = 10 cm

According to the question by using the formula we get,

$\leadsto \sf Area_{(Square)} =\: (10)^2$

$\leadsto \sf Area_{(Square)} =\: 10 \times 10$

$\leadsto \sf\bold{\red{Area_{(Square)} =\: 100\: cm^2}}$

$\therefore$ The area of the square is 100 cm².