Area of a Triangle
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Key Questions

The area of a triangle given two sides and an included angle is given as
#A=1/2ab si nC# where a and b are the sides and angle C is the included angle.Example: Given the triangle below, find the area.
Solution:
#A=1/2ab si nC#
#A=1/2(7)(9) si n30degrees#
#A=1/2(63)(1/2)#
#A=63/4# square units 
Heron's formula allows you to evaluate the area of a triangle knowing the length of its three sides.
The area#A# of a triangle with sides of lengths#a, b# and#c# is given by:#A=sqrt(spÃ—(spa)Ã—(spb)Ã—(spc))# Where
#sp# is the semiperimeter:#sp=(a+b+c)/2# For example; consider the triangle:
The area of this triangle is#A=(baseÃ—height)/2#
So:#A=(4Ã—3)/2=6#
Using Heron's formula:
#sp=(3+4+5)/2=6#
And:
#A=sqrt(6Ã—(65)Ã—(64)Ã—(63))=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.