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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