To find the area of a triangle without knowing the height, you can use the formula that involves the lengths of the sides of the triangle. Specifically, if you know the lengths of all three sides, you can apply Heron’s formula.
First, let’s denote the lengths of the sides of the triangle as a, b, and c. The steps are as follows:
- Calculate the semi-perimeter s of the triangle:
s = (a + b + c) / 2
- Then, use Heron’s formula to calculate the area A:
A = √(s * (s – a) * (s – b) * (s – c))
This formula works because it utilizes the lengths of the sides to determine the area without needing the height. Heron’s formula is especially useful when the height is difficult to measure or when dealing with irregular triangles.
In summary, just knowing the lengths of the sides is enough to find the area of a triangle using Heron’s formula!