Question

find the lateral surface area of cube if its diagonal root 6 cm

Answer 1

let the side be a
diagonal ^2=2a^2
So a^2=3
a=root 3
lateral surface area = 4a^2
=4×3=12cm&2

Answer 2

Answer:

$</p><p>Lateral \: surface \: area \: of \: the\\ \: cube =12 \:cm^{2}$

Step-by-step explanation:

$Let\\ \: edge \: of \: a \: cube = a \:cm$

$Diagonal (d) = \sqrt{6}\:(given)$

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

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

$\implies a = \sqrt{3}\: cm$

$Now,\\</p><p>Lateral \: surface \: area \: of \: the \: \\cube = 4a^{2}\\=4 \times \left(\sqrt{3}\right)^{2}\\=4\times 3\\=12 \: cm^{2}$

Therefore,

$</p><p>Lateral \: surface \: area \: of \: the\\ \: cube =12 \:cm^{2}$

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