For a triangle with base b and perpendicular height h, area = (b × h) ÷ 2. A triangle with a 12 cm base and a 7 cm height has area 42 cm².
First, make sure you have the right height
Choose any side as the base. The corresponding height must meet that side (or its extension) at a 90° angle. It is not automatically another side of the triangle. This distinction matters most for acute and obtuse triangles.
A worked example you can check mentally
Base = 12 cm; perpendicular height = 7 cm
12 × 7 = 84 cm²
84 ÷ 2 = 42 cm²
Why divide by two? Place a congruent copy of the triangle next to it. Together, the two triangles can form a parallelogram with base 12 and height 7. Each triangle covers half its area.
Does triangle type change the formula?
| Triangle | Where the height is | What to watch |
|---|---|---|
| Right triangle | One leg is perpendicular to the other. | The two legs can be b and h. |
| Acute triangle | Usually falls inside the figure. | Do not confuse altitude and sloped side. |
| Obtuse triangle | May fall outside the figure. | Extend the base line to meet the altitude. |
If you only know three sides: use Heron's formula
When a perpendicular height is not supplied, the three side lengths a, b and c can determine the area. First check that the lengths can form a triangle: the sum of any two must exceed the third.
Then calculate the semiperimeter s = (a + b + c) / 2, and apply:
For side lengths 5, 12 and 13 cm: s = (5 + 12 + 13)/2 = 15 cm. Then A = √(15 × 10 × 3 × 2) = √900 = 30 cm². Because 5² + 12² = 13², the same result comes from treating the 5 cm and 12 cm sides as perpendicular legs.
If you have the base and its perpendicular height, use bh/2—it is simpler and less error-prone. Heron's formula is useful when only three side lengths are known. The homepage triangle calculator uses base and height, not three sides.
Diagnose an unexpected result
If your area is exactly twice what you expected, you may have forgotten to divide by two. If the answer changes when you choose a different base, you likely used the wrong corresponding height. If the input lengths have different units, convert before multiplication.
For a deeper comparison of what area measures, see area versus perimeter. To calculate from dimensions, open the triangle area calculator.
Formula reference: OpenStax, Contemporary Mathematics.