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Hero's and Brahmagupta's Theorems - Lesson 11-8

Today we learned two formulas that were developed 2000-3000 years ago. The first was discovered by Hero of Alexandria and is therefore called Hero's Formula. It helps us to find the area of a triangle given the lengths of its three sides:

An example of using this to find the area of a triangle follows:

Simply apply the formula! First, you need to find the semiperimeter and then you can solve for the area.

The second formula was developed by a Hindu mathematician named Brahmagupta. His formula allows us to find the area of cyclic quadrilaterals:

Here's an example problem:

Again, start by finding the semiperimeter and then just use the formula: