How do you find surface area of a triangle?

Answer 1

The answer depends on what information you have and what level of mathematics you have reached.

If you have 3 sides, a, b and c: Let s = (a + b + c)/2

Area = sqrt[s*(s - a)*(s - b)*(s - c)]

Two sides and included angle, a, b and C

Area = 1/2*a*b*sin(C)

Two sides and non-included angle, a, b and A (or B)

use the sine rule to find the angle opposite the other known side. Use the sum of the angles of the triangle to find the included angle. Then as in previous case.

One side and two angles. a, B and C

Since the sum of the angles is 180 you effectively know all 3 angles. Use the sine rule to work out another side and then use the rule for a, b and C.

Equilateral triangle, sides a

then Area = [sqrt(3)*a^2]/4

Base, b and height, h:

Area = 1/2*b*h

There are others.