This triangle area calculator can help in determining the triangle area. The basic triangle area formula needs to have a base and height given, but what if we don't have it? How can we calculate the area of a triangle with 3 sides only? The triangle area calculator is here for you, give it a go! If you are still unsure how to find the area of a triangle, check the description below.
Triangle area formula
A triangle is one of the most basic shapes in geometry. The best known and the simplest formula, which almost everybody remembers from school is:
area = 0.5 * b * h, where
bis the length of the base of the triangle, and
his the height/altitude of the triangle.
However, sometimes it's hard to find the height of the triangle. In that cases, many other equations may be used, depending on what is known about the triangle:
Three sides (SSS)
If you know the lengths of all sides, use the Heron's formula:
area = 0.25 * √( (a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c) )
Two sides and the angle between them (SAS)
You can calculate area of a triangle easily from trigonometry:
area = 0.5 * a * b * sin(γ)
Two angles and a side between them (ASA)
There are different triangle area formulas versions - you can use for example trigonometry or law of sines to derive it:
area = a² * sin(β) * sin(γ) / (2 * sin(β + γ))
How to find the area of a triangle?
Assume that we know two sides and the angle between them:
- Type the first side length. It can be equal to 9 in in our example
- Enter the second triangle side. Let's choose 5 in.
- Determine the angle between two known sides. For example, 30 degrees.
- Watch our triangle area calculator performing all calculations for you! The area for our case is equal to 11.25 in².
Area of an equilateral triangle
To calculate the area of an equilateral triangle you only need to have the side given:
area = a² * √3 / 4
Although we didn't make a separate calculator for the equilateral triangle area, you can quickly calculate it in this triangle area calculator. Simply use the subpart for the area of a triangle with 3 sides - as you know that every side has the same length in an equilateral triangle. It's possible to calculate that area also in angle-side-angle or side-angle-side version - probably you remember that every angle in the equilateral triangle is equal to 60 degrees (π/3 rad).