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How to find area of a triangle enclosed by equations?

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?
Reply 1
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M14B
18
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
Reply 2
Avatar for lily628
lily628
OP
4
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 ???
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.
Reply 4
Avatar for lily628
lily628
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4
Original post by IrrationalRoot
It is.


oh lol, how can you tell?
Original post by lily628
oh lol, how can you tell?


One line has gradient 1, another has gradient -1, hence those two are perpendicular.
Use integration if you wanna go the difficult route
Reply 7
Avatar for lily628
lily628
OP
4
Original post by IrrationalRoot
One line has gradient 1, another has gradient -1, hence those two are perpendicular.


omg lol ofc
thank you!
Original post by lily628
omg lol ofc
thank you!


No probs :smile:.
Btw, working out the area from here is nice and easy if you do a quick sketch of the triangle on the coordinate plane.
Reply 9
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math42
20
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?
Original post by 1 8 13 20 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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