Management Aptitude Test 2016 Paper

(a) ∵ Area of a triangle = $\sqrt{\mathit{s}\left(\mathit{s}-\mathit{a}\right)\left(\mathit{s}-\mathit{b}\right)\left(\mathit{s}-\mathit{c}\right)}$

Here, a = 13, b = 20 and c = 21
∴ s = $\frac{13+20+21}{2}=\frac{54}{2}$ = 27
∴ Area of a triangle = $\sqrt{27\left(27-13\right)\left(27-20\right)\left(27-21\right)}$
= $\sqrt{27\times 14\times 7\times 6}$
= $\sqrt{3\times 3\times 3\times 7\times 2\times 7\times 2\times 3}$
= 9 × 2 × 7 = 126${\mathit{m}}^2$
So, area of both triangles = 2 x 126 = 252 ${\mathit{m}}^2$
Now area of sides = 30 x 13 + 30 x 20
= 390 + 600 = 990 ${\mathit{m}}^2$
and area of rectangle = 30 x 21 = 630 ${\mathit{m}}^2$
∴ Total surface area of triangular prism
= 252 + 990 + 630 = 1872 ${\mathit{m}}^2$