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.
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