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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.

Area of Triangles - 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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