Scalene Triangle Area

\[\begin{aligned} Area &= \sqrt{s(s-a)(s-b)(s-c)} \\ \text{where} \\ s &= \frac{a+b+c}{2} \end{aligned}\]

Variables

Areatriangle area (m²)

atriangle side a (m)

btriangle side b (m)

ctriangle side c (m)

ssemi-perimeter of the triangle (m)

This formula calculates the area of a scalene triangle using the lengths of its three sides.

It is commonly known as Heron's Formula and allows the area to be determined without knowing the height or any angles of the triangle.

A scalene triangle is a triangle where all three sides have different lengths.

Use this formula when:

- The three side lengths are known

- The triangle height is unknown

- Angle measurements are unavailable

- Solving geometry and surveying problems

- Working with irregular triangles

The formula works for any valid triangle.

If:

a = 7 m

b = 8 m

c = 9 m

Then:

s = (7+8+9)/2

s = 12 m

Area = √(12*(12-7)*(12-8)*(12-9))

Area = √720

Area ≈ 26.83 m²

- Geometry and trigonometry

- Civil engineering

- Land surveying

- Architecture and construction

- Physics calculations

- Computer graphics