Question

find the area of square in half of its diagonal is of length of 6cm​

Answer 1

The area of the square is 72 cm².

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Let's understand a few concepts:

To solve the given problem we will use the following formulas:

• $\boxed{\bold{Area \:of\:a\: square= side^2 = a^2}}$

• $\boxed{\bold{Diagonal \:of\:square = a\sqrt{2} }}$

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Let's solve the given problem:

Let "a" cm be the length of the side of the square.

∴ The diagonal of the square = $a\sqrt{2}$ cm

The half of the diagonal of the square is of the length of 6 cm​, so we can form an equation as,

$\frac{1}{2} \times diagonal\:of\:square = 6$

$\implies \frac{1}{2} \times a\sqrt{2} = 6$

$\implies a\sqrt{2} = 6\times 2$

$\implies a\sqrt{2} = 12$

$\implies a = \frac{2\times 2\times 3}{\sqrt{2} }$

$\implies a = \frac{\sqrt{2} \times \sqrt{2 } \times 2\times 3}{\sqrt{2} }$ . . . [∵ $\sqrt{2} \times \sqrt{2} = 2$]

$\implies a = \sqrt{2 } \times 2\times 3$

$\implies \bold{a =6 \sqrt{2 } \:cm}$

Now,

The area of the square is,

= a²

= $(6\sqrt{2} )^2$

= $6\times 6\times \sqrt{2} \times \sqrt{2}$

= $36 \times 2$

= $\bold{72\:cm^2}$

Thus, the area of the square is 72 cm².

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Answer 2

Step-by-step explanation:

answer is 72cm^2........................