Math
Triangle Area Calculator
Find triangle area using base and height, the three-side formula (Heron), or two sides and an angle. Shows step-by-step results.
Enter valid values above to calculate the area
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Triangle Area Formulas
Base & Height: A = ½ × b × h
Heron's Formula: s = (a+b+c)/2; A = √(s(s−a)(s−b)(s−c))
Two Sides & Angle (SAS): A = ½ × a × b × sin(C)
All three methods produce the same area for a valid triangle.
How to Use This Calculator
Select the method that matches the information you have, then enter the required values. For Heron's formula, the calculator checks that the three sides form a valid triangle using the triangle inequality.
For the SAS method, enter the angle in degrees (between 0 and 180).
Frequently asked questions
What are the three main ways to find the area of a triangle?
The most common methods are: (1) base and height — Area = ½ × base × height; (2) Heron's formula using all three side lengths; and (3) the SAS formula using two sides and the included angle — Area = ½ × a × b × sin(C).
What is Heron's formula?
Heron's formula finds the area from three side lengths a, b, c. First compute the semi-perimeter s = (a + b + c) / 2, then Area = √(s(s−a)(s−b)(s−c)).
What is the SAS triangle area formula?
When you know two sides and the angle between them, Area = ½ × side1 × side2 × sin(angle). The angle must be in degrees and is the angle formed between the two known sides.
Does the height have to be perpendicular to the base?
Yes. The height used in the base × height formula must be the perpendicular distance from the base to the opposite vertex. It is not the length of a slanted side.
What units does triangle area use?
Triangle area is measured in square units. If the base and height are in metres, the area is in square metres (m²). If in centimetres, the result is in square centimetres (cm²), and so on.