A triangle’s area is usually found with base × height ÷ 2, but sometimes the height is unknown. With Heron’s formula, you can calculate the area directly from the lengths of the three sides without knowing any angle or height. Adjust the three sides with the sliders and see how it works.
What is the semiperimeter (s)?: It is the sum of the three side lengths divided by 2—in other words, half the perimeter. Heron’s formula multiplies s by the values obtained by subtracting each side from s, then takes the square root to find the area.
When is it useful? In surveying, measuring angles can be difficult, while distances (side lengths) can often be measured with a tape measure. In situations like this, Heron’s formula is very useful because it lets you find an area using only the three side lengths, without measuring any angles.