Heron's Formula for the area of a triangleAlso called Hero's Formula
A method for calculating the area of a triangle when you know the lengths of all three sides.
Let a,b,c be the lengths of the sides of a triangle. The area is given by:
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where p is half the perimeter, or
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Try this Drag the orange dots to reshape the triangle. The formula shown will re-calculate the triangle's area using Heron's Formula
(If there is no image below, see support page.)
Heron was one of the great mathematicians of antiquity and came up with this formula sometime in the first century BC,
although it may have been known earlier. He also extended it to the area of quadrilaterals and higher-order polygons.
Things to Ponder
What is the area of a triangle whose sides are 12, 16 and 20 meters long?
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answer
96 sq meters. In the diagram above, try to create such a triangle
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| Challenge question:
What equilateral triangle would have the same area as a triangle with sides 6, 8 and 10?
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answer
One where each side has a length of 7.44
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Related triangle topics
General
Triangle types
Triangle centers
Congruence and Similarity
Triangle quizzes and exercises
(C) 2007 Copyright John Page
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