Question

The sides of a triangle are 39 cm, 25 cm and 56 cm. Find it's area.

Answer 1

We use Heron's formula to solve this problem.
Let a,b and c represent 3 sides of the triangle, such that a = 39 cm, b = 25 cm and c = 56 cm.
$\therefore$ a + b + c = 39 + 25 + 56 cm = 120 cm
Semi perimeter, s = ( a + b + c)/2 = 120/2 cm = 60 cm
Area of the triangle :-
= $\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{60(60-39)(60-25)(60-56)}c{m}^2=\sqrt{60\times 21\times 35\times 4}=\sqrt{2\times 2\times 3\times 5\times 3\times 7\times 5\times 7\times 2\times 2}=2\times 3\times 5\times 7\times 2c{m}^2=420c{m}^2$