Mensuration Practice Test 1

Sum of l, b and h = 24 cm
Length of its diagonal = 15
d = $\sqrt{{\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^1}$
${\left(15\right)}^2$ = ${\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^2$
${\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^2$ = 225
We know that
${\left(\mathit{a}+\mathit{b}+\mathit{c}\right)}^2$ = ${\mathit{a}}^2+{\mathit{b}}^2+{\mathit{c}}^2$ + 2(ab + bc + ca)
${\left(\mathit{l}+\mathit{b}+\mathit{h}\right)}^2$ = $\left({\mathit{l}}^2+{\mathit{b}}^2+{\mathit{h}}^2\right)$ + 2(lb + bh + hl)
${\left(24\right)}^2$ = 225 + 2 lb + bh + hl
576 = 225 + 2(lb + bh + hl)
Total surface area = 2(lb + bh + hl) = 576 − 225
= 351 $\mathit{c}{\mathit{m}}^2$