Question

Find the area of square whose diagonal is 7√3 cm.

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Answer 1

ᴀ = 24.5

ᴅɪᴀɢᴏɴᴀʟ 7

ᴍᴀy ᴛʜɪꜱ ᴀɴꜱᴡᴇʀ ʜᴇʟᴩ yᴏᴜ

ⓜⓐⓡⓚ ⓜⓔ. ⓐⓢ. ⓑⓡⓐⓘⓝⓛⓘⓢⓣ

Answer 2

The area of a square whose diagonal is 7√3 cm is 73.5 cm².

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Let's understand a few concepts:

To calculate the diagonal of the square we will use the following formula:

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

To calculate the area of the square we will use the following formula:

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

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Let's solve the given problem:

The diagonal of the square = 7√3 cm

So, we can form an equation as,

$a\sqrt{2} = 7\sqrt{3}$

$\implies a = \frac{7\sqrt{3}}{\sqrt{2} }$

$\implies a = \frac{7\sqrt{3}}{\sqrt{2} }\times \frac{\sqrt{2} }{\sqrt{2} }$

$\implies a = \frac{7\sqrt{3}}{2 }\times \sqrt{2}$

$\implies a = \frac{7\sqrt{6}}{2 }\:cm$

Therefore,

The area of the square is,

= $a^2$

= $\bigg( \frac{7\sqrt{6}}{2 }\bigg)^2$

= $\frac{7\times 7\times \sqrt{6}\times \sqrt{6} }{2\times 2 }$

= $\frac{49\times 6}{4 }$

= $\frac{294 }{4 }$

= $\bold{73.5\:cm^2}$

Thus, the area of the square whose diagonal is 7√3 cm is 73.5 cm².

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