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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:

Hero's Formula

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

  Example Problem using Hero's Formula

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

  Answer for Hero's Example Problem

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

Brahmagupta's Formula - Theorem 110

Here's an example problem:

  Example Problem using Brahmagupta's Formula


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

  Answer for Example Problem using Brahmagupta's Formula


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Class Notes
Lesson 11-1
Lesson 11-2
Lesson 11-3
Lesson 11-4
Quiz Topics
Lesson 11-5
Lesson 11-6
Lesson 11-7
Lesson 11-8
Test Topics
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