Area of a Triangle

When working out the area of a triangle the first thing you should always do is translate one of the points to (0,0). This will make things far more easier.

Example of translating:

Triangle with vertices:

(3,5)(1,2)(-2,-4) original values
-3 -5-3 -5-3 -5 subtract 3 from x-value & 5 from y-value
(0,0)(-2,-3)(-5,-9) this will translate one point onto (0,0)

(0,0)(x1,y1)(x2,y2)

three new vertices

The formula to find the area of a triangle with the vertices (0,0) (x1,y1) & (x2,y2)is:

Example:

Find the area of the triangle whose vertices are a(2,4) b(3,7) and c(-2,-3)

The first thing we have to do is translate one of the points onto (0,0):

a(-2,-3) b(2,4)c(3,7)
+2+3 +2+3+2+3 add 2 to x-value & 3 to y-value

a(0,0)b(4,7) c(5,10)

new vertices

(0,0) (x1,y1) (x2,y2)

write down values(x1,y1)(x2,y2)

It will be easier to find the area now.

write out the formula
sub in the values
work it out
=2.5 square units Area in square units

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