Question

The sides of a triangle are 56 cm , 60 cm and 52 cm then find its area using heron’s

formula​

Answer 1

Given :

• Sides of the triangle : 56cm, 60cm and 52cm.

To Find:

• Area of the triangle.

Solution:

heron's formula :-

$\tt \:{\boxed{ a = \sqrt{s(s - a)(s - b)(s - c)}}}$

• a = area of the triangle.
• s = semi-perimeter
• a, b, c = sides of the triangle.

semi-perimeter of the triangle :

⟹ 1/2 × ( a + b + c)

⟹ 1/2 ( 56cm + 60cm + 52cm)

⟹ 1/2 ( 168cm)

⟹ 84cm

substitute the values :-

$\tt \: \sqrt{84cm(84cm- 56cm)(84cm - 60cm)(84cm - 52cm)}$

$➞\tt \sqrt{84cm(28cm)(24cm)(32cm)}$

$➞\tt \: \sqrt{1806336 {cm}^{4} }$

$➞\tt \: 1344 {cm}^{2}$

1344cm² is the area of the triangle