How to Figure the Surface Area of a Triangle

Heron's formula finds the area of irregular triangles.

The surface area of a triangle is half the product of its base and height. This makes finding the area easy when you know these measurements, such as when two sides meet at a right angle. But in some triangles, you need additional calculations just to find the height. In other triangles, the height is difficult to find even with trigonometry or Pythagoras' theorem. With these triangles, and with any other triangle as well, you can use an alternate formula for finding the shape's area.

Instructions

1. Add the length the triangle's three sides. For example, if a triangle has sides of 4, 12 and 9 inches, then 4 + 12 + 9 = 25.

2. Divide this answer by 2 -- 25 / 2 = 12.5.

3. Compute the product of the differences between this answer and each of the triangle's lengths. Continuing this example, (12.5 - 4) --- (12.5 - 12) --- (12.5 - 9) = 14.875.

4. Multiply this product by the answer from Step 2 -- 14.875 --- 12.5 = 185.938.

5. Find the square root of this answer 185.938^0.5 = 13.64 square inches. This is the triangle's surface area.

References

• University of Georgia; Problem Solving With Heron's Formula; James W. Wilson; October 1986
• University of Kentucky; Heron's Formula for Triangular Area; Christy Williams et. al.

Resources

• University of Illinois; Triangle Area Calculator; James P. Dildine; August 1999
• University of Virginia: Geometrical Proof of Heron's Formula