Question

The side of triangle are 56cm, 60cm and52cm long. Then the area of the triangle is? By Herin's formula​

Answer 1

Answer:

Given :-

• The side of triangle are 56 cm, 60 cm and 52 cm long.

To Find :-

• What is the area of the triangle.

Solution :-

First, we have to find the semi-perimeter of a triangle :

As we know that :

✫ Semi-Perimeter = a + b + c/2 ✫

Given :

• a = 56 cm
• b = 60 cm
• c = 52 cm

According to the question by using the formula we get,

➼ Semi-Perimeter = 56 + 60 + 52/2

➼ Semi-Perimeter = 116 + 52/2

➼ Semi-Perimeter = 168/2

➲ Semi-Perimeter = 84 cm

Now we have to find the area of a triangle by using Heron's Formula :

As we know that :

✰ Area Of Triangle = √s(s - a)(s - b)(s - c)

According to the question by using the Heron's formula we get,

➣ Area Of Triangle = √84(84 - 56)(84 - 60)(84 - 52)

➣ Area Of Triangle = √84(28)(24)(32)

➣ Area Of Triangle = √84 × 28 × 24 × 32

➣ Area Of Triangle = √1806336

➣ Area Of Triangle = √1344 × 1344

➠ Area Of Triangle = 1344 cm²

∴ The area of a triangle is 1344 cm².

Answer 2

Given:

The sides of the triangle- 56cm, 60cm and 52cm

To find:

Area of the triangle by Heron's formula.

Solution:

Heron's formula for finding the area of the triangle is:

$\sqrt{s(s - a)(s - b)(s - c)}$

where, s= semi perimeter of the triangle and a, b, c are the three sides of the triangle.

So, first, we find the semi perimeter of the triangle by using this formula-

$s = \frac{a + b + c}{2}$

$= \frac{56 + 60 + 52}{2}$

$= \frac{168}{2}$

$= 84cm$

So, by applying Heron's formula, we have:

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

$= \sqrt{84(28)(24)(32)}$

$= \sqrt{1806336}$

$= 1344 {cm}^{2}$

Hence, using Heron's formula, area of the given triangle is 1344 square centimetres.