Triangle Area Calculator

Area = 1/2 * base * height. The base is any chosen side, and the height is the segment drawn perpendicular from the opposite vertex to that base. Simply multiply base by height and divide the result by two.

Every triangle is half of a parallelogram with the same base and height. The area of a parallelogram is base times height, so the triangle area is exactly half of that value. That is why the factor 1/2 appears in the formula.

Use the Heron formula. Compute the semi-perimeter s = (a+b+c)/2, then area = square root of s*(s-a)*(s-b)*(s-c). This formula does not need the height and works for any triangle that satisfies the triangle inequality.

The Heron formula computes triangle area only from the lengths of the three sides, without angles or height. It is area = square root of s*(s-a)*(s-b)*(s-c), where s is the semi-perimeter. It is useful when sides are easier to measure than the height.

In a right triangle the two legs are perpendicular, so one acts as the base and the other as the height. The area is 1/2 * leg1 * leg2. This is the simplest case, because the height does not need to be found separately.

Yes. Any side can serve as the base, but you must use the height dropped onto that side. The area stays the same regardless of the choice, because a larger base corresponds to a smaller height and vice versa. The base and height just have to match.

The area is in square units of the input data. Base and height in centimetres give an area in cm2, in metres give m2. The calculator returns a numeric value, so you choose the unit according to your data.

The product a * h is the area of a parallelogram with the same base and height, that is twice the triangle area. The calculator shows it as a helper result so it is easier to understand the division by two in the area formula.

Yes. The formula 1/2 * base * height holds for every triangle: acute, right and obtuse. In an obtuse triangle the height onto some sides can fall outside the triangle, on the extension of the base, but its length is still used in the same formula.

Compare results from different methods: if you know the sides and height, compute the area with 1/2 * a * h and with the Heron formula — both should give the same result. Also make sure the height is measured perpendicular to the chosen base.