Question

The lengths of the three sides of a triangular field are 40 m, 24 m and 32 m respectively. The area of the triangle is
(a) 480 m²
(b) 320 m²
(c) 384 m²
(d) 360 m²

Answer 1

(c) 384 m²

$$\begin{gathered} \mathrm{Let}: \\ a=40\mathrm{m},b=24\mathrm{m}\mathrm{and}c=32\mathrm{m} \\ s=\frac{a+b+c}{2}=\frac{40+24+32}{2}=48\mathrm{m} \\ \mathrm{By}\mathrm{Heron}\text{'}\mathrm{s}\mathrm{formula},\mathrm{we}\mathrm{have}: \\ \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{48(48-40)(48-24)(48-32)} \\ =\sqrt{48\times 8\times 24\times 16} \\ =\sqrt{24\times 2\times 8\times 24\times 8\times 2} \\ =24\times 8\times 2 \\ =384{\mathrm{m}}^2 \end{gathered}$$