Triangle Area Calculator

The simplest formula is $A = \frac{1}{2} \times \text{base} \times \text{height}$. The height must be perpendicular to the chosen base. Any side can serve as the base — the height changes accordingly, but the area stays the same.

Heron's formula calculates triangle area from all three side lengths: $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \frac{a+b+c}{2}$ is the semi-perimeter. Use it when you know all three sides but not the perpendicular height.

Use the SAS formula: $A = \frac{1}{2} \times a \times b \times \sin(C)$, where $a$ and $b$ are two sides and $C$ is the included angle between them. The sine converts the angle into the effective perpendicular height.

Yes. $A = \frac{1}{2} \times \text{base} \times \text{height}$ works for right, acute, and obtuse triangles. For obtuse triangles, the height falls outside the triangle when dropped from certain vertices, but the formula still gives the correct area.

Use the Shoelace formula: $A = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$. This is especially useful in coordinate geometry and computer graphics where vertices are given as $(x, y)$ pairs.