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# How to find area of a triangle enclosed by equations?

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1. I was just wondering what the method would be for this? An example is:

y - x = 2
x + y = 6
3x + y = 6

i was thinking about using simultaneous equations, would that be along the right lines?
2. (Original post by lily628)
I was just wondering what the method would be for this? An example is:

y - x = 2
x + y = 6
3x + y = 6

i was thinking about using simultaneous equations, would that be along the right lines?
Find their intersections
3. (Original post by M14B)
Find their intersections
right, so i got (0,6), (1,3) and (2,4)

but how am i supposed to find the area from this? it isn't a right angled triangle so i can't use base x height / 2 but don't have any angles so ???
4. (Original post by lily628)
right, so i got (0,6), (1,3) and (2,4)

but how am i supposed to find the area from this? it isn't a right angled triangle so i can't use base x height / 2 but don't have any angles so ???
It is.
5. (Original post by IrrationalRoot)
It is.
oh lol, how can you tell?
6. (Original post by lily628)
oh lol, how can you tell?
One line has gradient 1, another has gradient -1, hence those two are perpendicular.
7. Use integration if you wanna go the difficult route
8. (Original post by IrrationalRoot)
One line has gradient 1, another has gradient -1, hence those two are perpendicular.
omg lol ofc
thank you!
9. (Original post by lily628)
omg lol ofc
thank you!
No probs .
Btw, working out the area from here is nice and easy if you do a quick sketch of the triangle on the coordinate plane.
10. One way which seems fairly quick is to split it into two triangles each with horizontal base

(Original post by lily628)
I was just wondering what the method would be for this? An example is:

y - x = 2
x + y = 6
3x + y = 6

i was thinking about using simultaneous equations, would that be along the right lines?
11. (Original post by 13 1 20 8 42)
One way which seems fairly quick is to split it into two triangles each with horizontal base
Yeah but then you have to work out the length of the horizontal base.
Anyway once you've sketched it, it's easy to work out the lengths of the legs in your head very quickly.

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