Heron's formula  Perimeter, area, and volume  Geometry  Khan Academy  Summary and Q&A
TL;DR
Heron's Formula allows you to find the area of a triangle when only given the lengths of its sides.
Questions & Answers
Q: How do you find the area of a triangle when only the lengths of its sides are given?
To find the area of a triangle with given side lengths, you can use Heron's Formula. First, calculate the semiperimeter (S) by adding all the side lengths and dividing the sum by 2. Then, use the formula: area = √(S * (S  a) * (S  b) * (S  c)), where a, b, and c are the side lengths.
Q: What is Heron's Formula?
Heron's Formula is a mathematical formula used to find the area of a triangle when only the lengths of its sides are known. It involves calculating the semiperimeter and using it in a square root expression to find the area.
Q: What are the advantages of using Heron's Formula?
Heron's Formula is advantageous because it allows you to find the area of a triangle without knowing its height. It is also applicable to any type of triangle, whether it is equilateral, scalene, or isosceles.
Q: How can Heron's Formula be applied practically?
Heron's Formula can be applied practically when you need to find the area of a triangle but only have access to its side lengths. It is particularly useful in geometry and engineering, where accurate area calculations are necessary.
Summary & Key Takeaways

The area of a triangle can be easily calculated if the base and height are given.

Heron's Formula allows you to find the area of a triangle when only the lengths of its sides are given.

Heron's Formula involves calculating the semiperimeter of the triangle and then using it to find the area.