SSC CGL Tier II 25 Oct 2015 Paper 1

(2) In ΔABC,
a = 13 cm.,b = 20 cm., c = 21 cm., Semi-perimeter $=\mathit{s}=\frac{\mathit{a}+\mathit{b}+\mathit{c}}{2}$ $=\left(\frac{13+20+21}{2}\right)\mathrm{cm}.$$=\frac{54}{2}=27\mathit{c}\mathit{m}$
∴ Area of DABC = Area of the base of prism
$=\sqrt{\mathit{s}\left(\mathit{s}-\mathit{a}\right)\left(\mathit{s}-\mathit{b}\right)\left(\mathit{s}-\mathit{c}\right)}$
$=\sqrt{27\left(27-13\right)\left(27-20\right)\left(27-21\right)}$
$=\sqrt{27\times 14\times 7\times 6}$
$=\sqrt{3\times 3\times 3\times 2\times 7\times 7\times 2\times 3}$
$=3\times 3\times 2\times 7=126\mathrm{sq}.\mathrm{cm}$
∴ Volume of prism = Area of base × height
= 126 × 9 = 1134 cu. cm