Heron’s formula

Definition

Heron's formula is used to find the area of a triangle when the lengths of all three sides are known. It is useful for non-right triangles and can be expressed as $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter of the triangle.

5 Must Know Facts For Your Next Test

1. Heron's formula: $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $a$, $b$, and $c$ are the side lengths, and $s = \frac{a+b+c}{2}$.
2. The semi-perimeter $s$ is half the sum of the triangle's sides: $s = \frac{a+b+c}{2}$.
3. Heron's formula works for any type of triangle, not just right triangles.
4. You must first calculate the semi-perimeter before applying Heron's formula.
5. It's particularly useful when you don't know any angles of the triangle.

Review Questions

• What is Heron's formula for finding the area of a triangle?
• How do you calculate the semi-perimeter in Heron's formula?
• Can Heron's formula be used for right triangles?

Related terms

Semi-perimeter: Half of the perimeter of a triangle, calculated as $\frac{a+b+c}{2}$ where $a$, $b$, and $c$ are the side lengths.

Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$, relates the lengths of sides in any triangle to its angles.

Non-right Triangle: A triangle that does not have a 90-degree angle. Requires methods like Heron's formula or Law of Cosines for solving.