How to Find the Area of a Triangle

The area of a triangle measures how much space is inside it. Unlike rectangles (length × width), triangles use a slightly different formula because they're essentially half a rectangle.

The formula

The base is any side of the triangle. The height (altitude) is the perpendicular distance from that base to the opposite vertex.

Example 1: Simple triangle

A triangle has a base of 10 cm and a height of 6 cm. Find the area.

Area = 30 cm²

Example 2: Right triangle

A right triangle has legs of 5 in and 12 in. Find the area.

In a right triangle, the two legs serve as the base and height (they're already perpendicular).

Example 3: Obtuse triangle

A triangle has a base of 14 m. The height, measured from the base to the top vertex, is 8 m. Find the area.

Even when the height falls outside the triangle (for obtuse triangles), the formula stays the same.

Example 4: Finding a missing measurement

A triangle has an area of 24 cm² and a base of 8 cm. What is the height?

Common mistakes

Forgetting to halve: A = base × height gives you a rectangle's area. A triangle is half of that, so don't forget the ½.

Using the slant side as height: The height must be perpendicular to the base. It's NOT the slant side of the triangle (unless the triangle is a right triangle and you use the legs).

Units: Area is always in square units (cm², m², in²). If the base is in cm and the height is in cm, the area is in cm².

Quick reference

• A = ½ × b × h
• Height must be perpendicular to the base
• Works for all triangle types
• For right triangles, the legs are the base and height
• Area is always in square units

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