How Do You Calculate the Area of a Triangle?

# How Do You Calculate the Area of a Triangle?

Find the length of the triangle's base and height, multiply them together, and divide the product by two to find the area. Find the length of all sides of the triangle or the length of two sides and the angle between those two sides if the base and height are unavailable.

1. Multiply the base and the height, and divide the product by two

Read the parameters of the problem, looking for the base and height. Plug those two numbers into the formula to calculate the triangle's area. Use the Pythagorean theorem to calculate the height if you know where the altitude (the line from one angle that forms a right angle with the opposite side) meets the base.

2. Use Heron's Formula if you know all three sides

Apply Heron's Formula to calculate the area of the triangle if you do not know the base and height. Calculate the semiperimeter (s = 1/2(a+b+c)), where a, b and c are the lengths of the three sides of the triangle. Find the area by taking the square root of [s(s-a)(s-b)(s-c)].

3. Use the sine of the included angle

Multiply the lengths of two sides by the sine of the included angle, and divide the product by two to get the area of a triangle. Consider the example of triangle ABC, in which angle C is included between sides a and b. Take the sine of angle C, and multiply it by the lengths of sides a and b to find the area.