Area of a Triangle
Key Questions
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Heron's formula allows you to evaluate the area of a triangle knowing the length of its three sides.
The areaA of a triangle with sides of lengthsa, b andc is given by:A=sqrt(sp×(sp-a)×(sp-b)×(sp-c)) Where
sp is the semiperimeter:sp=(a+b+c)/2 For example; consider the triangle:
The area of this triangle isA=(base×height)/2
So:A=(4×3)/2=6
Using Heron's formula:
sp=(3+4+5)/2=6
And:
A=sqrt(6×(6-5)×(6-4)×(6-3))=6 The demonstration of Heron's formula can be found in textbooks of geometry or maths or in many websites. If you need it have a look at:
http://en.m.wikipedia.org/wiki/Heron%27s_formula -
You can use it whenever you know the lengths of all three sides of a triangle.
I hope that this was helpful.