# How to find the area of a triangle without the height?

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane.

## Answer: We will use Heron’s formula to find the area of a triangle without the height.

Let us look at how to use Heron’s formula in the explanation below.

**Explanation:**

Heron's formula is used to find the area of a triangle when the length of the 3 sides of the triangle is known. The perimeter of a triangle is the distance covered around the triangle and is calculated by adding lengths of all three sides of a triangle.

Heron's formula to find the area of the triangle is:

Area = √S(S−a)(S−b)(S−c)

'S' is the semi-perimeter which is given by (A + B + C)/2

Let’s solve an example:

A = 8, B = 6, C = 12

Let's find the area of a triangle with the help of Heron's formula.

A = √S(S−a)(S−b)(S−c)

First, we need to find the value S.

So, we use this: S = (A + B + C)/2

⇒ S = (8 + 6 + 12)/2

⇒ S = 13

Now, put the value of S in Heron's formula.

⇒ A = √13(13−8)(13−6)(13−12)

⇒ A = √455 = 21.33

### Thus, Heron's formula to find the area of the triangle (without height) is: A = √S(S−a)(S−b)(S−c)

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