Triangle Area Calculator
A triangle with a base of 10 and a height of 6 has an area of 30, half of the 10 x 6 rectangle around it. This triangle area calculator handles the three standard cases: base and height, all three sides using Heron's formula, and two sides with the angle between them. Pick whichever matches the measurements you actually have.
Quick answer
The classic formula is area = base x height / 2, half the enclosing rectangle.
Area
30
What this tells you
- •The classic formula is area = base x height / 2, half the enclosing rectangle.
- •Know all three sides but no height? Heron's formula gets the area from the sides alone.
- •Know two sides and the angle between them? Area = a x b x sin(angle) / 2.
- •All three methods give the same answer for the same triangle, so use the one matching your data.
How to Use
- 1Choose the method that fits what you know about the triangle.
- 2Enter the measurements. For base and height, the height must be perpendicular to the base.
- 3For three sides, any two sides together must be longer than the third.
- 4Read the area in the square of whatever unit you entered.
How It Works
Formula
A = b x h / 2, or A = sqrt(s(s-a)(s-b)(s-c)) with s = (a+b+c)/2The base-height formula works because any triangle is exactly half of a parallelogram with the same base and height. Heron's formula uses the semi-perimeter s. For sides 5, 6, 7, s is 9, and the area is the square root of 9 x 4 x 3 x 2, which is sqrt(216), about 14.7. The trigonometric version a x b x sin(C) / 2 works because b x sin(C) is the height when a is the base.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Base 10, height 6
Multiply 10 by 6 to get 60, then halve it.
Sides 5, 6, and 7
Heron's formula with s = 9 gives sqrt(9 x 4 x 3 x 2) = sqrt(216) = 14.697.
Sides 8 and 5 with a 60 degree angle
8 x 5 x sin(60) / 2 = 40 x 0.866 / 2 = 17.32.
Triangle Areas for Common Dimensions
Base and height pairs with their areas.
| Base | Height | Area |
|---|---|---|
| 4 | 3 | 6 |
| 10 | 6 | 30 |
| 12 | 8 | 48 |
| 15 | 10 | 75 |
| 20 | 14 | 140 |
Common mistakes
- Using a slanted side as the height. The height is the perpendicular distance from the base to the opposite corner, not the length of a side.
- Forgetting to halve. Base times height gives the surrounding parallelogram, and the triangle is half of it.
- Entering three sides that cannot form a triangle. Sides 1, 2, and 5 fail because 1 + 2 is less than 5.
- Using the wrong angle in the trig method. The angle must sit between the two sides you entered.