If two identical solid cubes of side '$\mathrm{a}$' are joined end to end, then find the total surface area of the resulting cuboid.

If two cubes are joined end to end, then the resulting shape will be a cuboid.

∴ Length of the cuboid, $\mathrm{l}=\mathrm{a}+\mathrm{a}=2\mathrm{a}$

Breadth of the cuboid, $\mathrm{b}=\mathrm{a}$

Height of the cuboid, $\mathrm{h}=\mathrm{a}$

 The total surface area of the resulting cuboid

$=2(\mathrm{lb}+\mathrm{bh}+\mathrm{hl})$

$=2(2\mathrm{a}\times \mathrm{a}+\mathrm{a}\times \mathrm{a}+\mathrm{a}\times 2\mathrm{a})$

$=2\left(2{\mathrm{a}}^2+{\mathrm{a}}^2+2{\mathrm{a}}^2\right)$

$=2\times 5{\mathrm{a}}^2$

$=10{\mathrm{a}}^2$