The lengths of three sides of a triangle are 20 cm, 16 cm and 12 cm.
Question:

The lengths of three sides of a triangle are 20 cm, 16 cm and 12 cm. The area of the triangle is
(a) 96 cm2
(b) 120 cm2
(c) 144 cm2
(d) 160 cm2

Solution:

(a) 96 cm2

Let:

$a=20 \mathrm{~cm}, b=16 \mathrm{~cm}$ and $c=12 \mathrm{~cm}$

$s=\frac{a+b+c}{2}=\frac{20+16+12}{2}=24 \mathrm{~cm}$

By Heron’s formula, we have :

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

$=\sqrt{24(24-20)(24-16)(24-12)}$

$=\sqrt{24 \times 4 \times 8 \times 12}$

$=\sqrt{6 \times 4 \times 4 \times 4 \times 4 \times 6}$

$=6 \times 4 \times 4$

$=96 \mathrm{~cm}^{2}$