Two ways to find the area
Base and height: area = ½ × base × height, where the height is measured at right angles to the base. A triangle with a 10 cm base and a 5 cm height has an area of 25 cm²: half of the 10 × 5 rectangle around it.
Three sides (Heron's formula): when the height is unknown, as with a plot of land measured along its edges, use s = (a + b + c) ÷ 2 and area = √(s(s − a)(s − b)(s − c)). For sides 3, 4 and 5: s = 6 and area = √(6 × 3 × 2 × 1) = 6.
Angles from the sides
With three sides the page also finds the angles using the law of cosines. The 3-4-5 triangle has angles of about 36.87°, 53.13° and exactly 90°, which is why builders use it to set out right angles.
When sides don't fit
A triangle exists only if each side is shorter than the other two together. Sides 1, 2 and 3 lie flat in a line and enclose no area.
How this works
In base-and-height mode the page multiplies the base by the height and halves it. In three-sides mode it checks the triangle inequality and applies Heron's formula in a rearranged form that stays accurate for very thin triangles, then computes each angle from the law of cosines. Results carry your unit, squared for the area. Everything runs in your browser.
Frequently asked
What is the formula for the area of a triangle?
Area = ½ × base × height, or Heron's formula when you know the three sides.
How do I find the height of a triangle?
Height = 2 × area ÷ base. With three sides, compute the area with Heron's formula first.
What is Heron's formula?
Area = √(s(s−a)(s−b)(s−c)), where s is half the perimeter.
Why does the calculator say my triangle is impossible?
One side is as long as or longer than the other two combined, so the sides cannot close into a triangle.
Sources
Reviewed Oct 17, 2026 · test vectors fixtures/calculators/math/area/triangle/