Area of a Triangle Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the area of a triangle?

Answer

Area of a triangle
A = ½ · a · h

Here a is the side (or base), h is the height, perpendicular to the base. The result comes out in square units.

Where the formula comes from

A = ½ · a · h

Take a second copy of the triangle, turn it 180° and join it to the first along one side: the two together make a parallelogram with base a and height h. The triangle is exactly half of it.

Worked examples

Let a = 10, h = 6. Then the area of a triangle = 30 square units.

Let a = 7.5, h = 4. Then the area of a triangle = 15 square units.

The common mistake

Using a slanted side as the height. The height is the perpendicular distance from the base to the opposite vertex, and in an obtuse triangle the two heights drawn to the sides next to the obtuse angle fall outside the triangle — you have to extend the base to meet them.

Other quantities: Triangle

Related Calculations

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the area of a triangle? (The answer is: A = ½ · a · h). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula (h = 6)

If a =Area
13 square units
26 square units
39 square units
412 square units
515 square units
1030 square units

FAQ

What is the formula for the area of a triangle?

Area of a triangle A = ½ · a · h

Where does this formula come from?

Take a second copy of the triangle, turn it 180° and join it to the first along one side: the two together make a parallelogram with base a and height h. The triangle is exactly half of it.

What is the most common mistake here?

Using a slanted side as the height. The height is the perpendicular distance from the base to the opposite vertex, and in an obtuse triangle the two heights drawn to the sides next to the obtuse angle fall outside the triangle — you have to extend the base to meet them.

How do I use this formula?

Put your own numbers in place of the letters. With a = 7.5, h = 4, for instance, the formula A = ½ · a · h gives = 15 square units.

See Also