Area of Geometric Shapes Calculator
Calculate the area and perimeter of geometric shapes online: square, rectangle, triangle, circle, trapezoid, rhombus, regular hexagon and ellipse.
Maths
Calculator · Maths
Triangle Area Calculator
Enter the base and height of a triangle, and the calculator returns the area from the formula area = 1/2 * base * height, plus the product of base and height, which equals the area of the corresponding parallelogram.
How we calculate triangle area
Area = 1/2 * base * height, where the height is drawn perpendicular to the chosen base. The product of base and height (a * h) equals the area of a parallelogram and is twice the triangle area. For three sides use Heron formula.
Example: base 10, height 5
For a triangle with base 10 and height 5: product of base and height = 10 * 5 = 50. Area = 1/2 * 50 = 25. The unit of area is the square of the input unit, e.g. for centimetres the result is 25 cm2.
Frequently asked questions
How do I calculate the area of a triangle from base and height?
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.
Where does the 1/2 in the formula come from?
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.
What if I do not know the height, only the three sides?
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.
What is the Heron formula?
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.
How is the area of a right triangle calculated?
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.
Can any side be the base of the triangle?
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.
In what units is the area expressed?
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.
What does the product of base and height mean in the results?
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.
Does the formula work for an obtuse triangle?
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.
How can I verify the calculated area?
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.
Indicative result
The calculator uses the base and height formula. When you only know the three sides, apply the Heron formula described in the questions below.