Question

The length of a diagonal of a square is 8√2 cm. Find its area.​

Answer 1

Answer:

Answer. side = 8 cm. = 64 cm ^2.

Step-by-step explanation:

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Answer 2

$\large\sf\underline{Given\::}$

• Length of a diagonal of square = 8√2 cm

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$\large\sf\underline{To\:find\::}$

• Area of the square

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$\large\sf\underline{Understanding\:the\:concept\::}$

In the question we are given the diagonal of a square as 8√2 cm. We are asked to find the area of the square. We do know that area of a square is $\sf\:(side) ^{2}$ . But wait we are not provided with the length of side of the square. So in order to solve this problem we first need to find the length of side of the square. We will proceed by using the formula for diagonal of square and the given value of diagonal. Doing so we will get the length of side of square and using the area formula we can easily solve this problem. Let's begin!

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$\large\sf\underline{Solution\::}$

We know,

◎ $\small{\underline{\boxed{\mathrm\green{Diagonal\:of\:☐\:=\sqrt{2} \times side }}}}$

• Substituting the value in the formula

$\sf\:8\sqrt{2}=\sqrt{2} \times side$

$\sf\implies\:\frac{8\sqrt{2}}{\sqrt{2}}=side$

$\sf\implies\:\frac{8\cancel{\sqrt{2}}}{\cancel{\sqrt{2}}}=side$

$\sf\implies\:8=side$

$\large{\mathfrak\red{\implies\:side\:=\:8\:cm}}$

So now we do know the length of side of a square ,

Let's use the formula for area and solve it :

◎ $\small{\underline{\boxed{\mathrm\green{Area\:of\:☐\:=\:(side)^{2}}}}}$

• Substituting the value of side in the formula

$\sf\implies\:Area\:=(8)^{2}$

$\large{\mathfrak\red{\implies\:Area\:=\:64\:sq.cm}}$

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!! Hope it helps !!