Triangle Area Calculator
Calculate triangle area three ways, depending on which measurements you have.
How to use the Triangle Area Calculator
- Choose the method.
- Enter the base.
- Enter the height (perpendicular to base).
- Enter the side a.
- Enter the side b.
- Enter the side c.
- Enter the angle between a and b.
- Press Calculate. The result updates automatically as you type.
About the Triangle Area Calculator
Every triangle is half of a parallelogram with the same base and height, which is where the familiar ½ × base × height comes from. The catch is that the height must be measured at a right angle to the base, and in the real world you often know the side lengths instead. Heron's formula handles that case using only the three sides, and the SAS formula works when you know two sides and the angle between them, as with a surveyor's measurements or a triangular garden bed.
Any side can serve as the base, as long as the height is measured to that same side. Three lengths only form a triangle if each one is shorter than the sum of the other two; the calculator warns you when they do not.
Formula
Area = ½ × base × height
Heron: s = (a + b + c) ÷ 2, Area = √(s(s − a)(s − b)(s − c))
SAS: Area = ½ × a × b × sin C
For the side-based methods the calculator also finds the angles with the law of cosines: cos A = (b² + c² − a²) ÷ 2bc.
Example calculation
Using the default values:
- Method = Base and height
- Base = 10
- Height (perpendicular to base) = 6
the calculator returns:
- Area: 30 square units
Frequently asked questions
How do I find the area of a triangle without the height?
Use Heron's formula if you know all three sides, or ½ab·sin C if you know two sides and the angle between them.
What is the area of a triangle with sides 7, 8 and 9?
s = 12, so the area is √(12 × 5 × 4 × 3) = √720 ≈ 26.83 square units.
Why is triangle area divided by 2?
Two copies of any triangle fit together to make a parallelogram whose area is base × height, so one triangle is half of that.
Last updated: · Category: Math calculators