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Area of Triangles

You know that Area = base x height / 2, but what other ways are there to find the area of a triangle? Brace yourself for some potent formulae.

Heron's Formula

         

What is the area of a triangle with side lengths \(9,12,\) and \(15?\)

What is the area of a triangle with side lengths \(13, 14,\) and \(15?\)

What is the area of a triangle with side lengths \(9, 11,\) and \(10?\)

A triangle has perimeter 14 and area \(2\sqrt{14}.\) If the shortest side has length 3, find the positive difference between the lengths of other two sides. Give your answer to 3 decimal places.

What is the area of a triangle with side lengths \(3,5,\) and \(7?\)

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