Question

Find the area of the triangle with sides 35 cm, 54 cm and 61 cm.

Answer 1

We will use Heron's formula to find the area of the triangle.
Here, a = 35 cm, b = 54 cm and c = 61 cm. Now
$s=\frac{a+b+c}{2}=\frac{35+54+61}{2}=\frac{150}{2}=75$
Therefore
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \\ =\sqrt{75\left(75-35\right)\left(75-54\right)\left(75-61\right)} \\ =\sqrt{75\times 40\times 21\times 14} \\ =4\times 3\times 5\times 7\sqrt{5} \\ =420\sqrt{5} \end{gathered}$$
Hence, the area of the required triangle is $420\sqrt{5}\mathrm{sq}.\mathrm{units}$.