How to Find the Area of a Triangle

The area of a triangle depends on only two lengths: a base, and the height measured perpendicular to that base. The same formula works for acute, obtuse and right triangles alike.

• $S$ — the area
• $b$ — the length of the base
• $h$ — the height, measured perpendicular to the base

Example

With the calculator's defaults, a base of $b = 4$ and a height of $h = 3$:

The area is 6. If the lengths are in centimetres, the area is in square centimetres.

Why the formula halves the product

Take a second copy of the triangle, rotate it by 180 degrees and join it to the first. Together they form a parallelogram with base $b$ and height $h$, whose area is $b h$. The triangle is exactly half of that, which gives $\dfrac{1}{2} b h$.

Watch out

The height is the perpendicular distance from the base to the opposite vertex, not the length of a slanted side. In an obtuse triangle the foot of that perpendicular falls outside the base, on its extension, and the formula still holds. Any side can play the role of the base, provided you pair it with the height that belongs to it; the area comes out the same every time. Keep the base and the height in the same unit.