Triangle Area Calculator

A Triangle Is Half of a Rectangle

Here is the idea that makes the formula click: a triangle is exactly half of a rectangle. Draw a rectangle around a triangle so they share the same base and the same height, and the triangle fills precisely half of it. That is why you multiply base by height and then take half:

$$\text{area} = \tfrac{1}{2} \times \text{base} \times \text{height}$$

The height is the straight-up (perpendicular) distance from the base to the top corner - the dashed line in the figure - not the length of a slanted side. If you only know the three side lengths and no height, Heron’s formula finds the area for you.

The Formulas

$$\text{area} = \tfrac{1}{2} \times \text{base} \times \text{height}$$

From the three sides (Heron’s formula), with $s = \dfrac{a + b + c}{2}$:

$$\text{area} = \sqrt{s(s - a)(s - b)(s - c)}$$

How to Use It

1. Choose base and height or three sides.
2. Enter the measurements.
3. Read the area and the steps.

Worked Examples

Method	Inputs	Area
Base and height	base 6, height 4	12
Base and height	base 10, height 7	35
Three sides	3, 4, 5	6
Three sides	6, 8, 10	24

FAQ

How do you find the area of a triangle?

Multiply the base by the height and halve it: $\tfrac{1}{2} \times 6 \times 4 = 12$.

What is Heron’s formula?

When you know all three sides, $\text{area} = \sqrt{s(s - a)(s - b)(s - c)}$, where s is half the perimeter. It needs no height.

What counts as the height?

The perpendicular distance from the base to the opposite corner — not the length of a slanted side.