Differentiation - find triangle area question

Rhys_M

11

Hi, can someone tell me how I would find the area of ABP in the question below please?
Thank you

(edited 2 years ago)

Reply 1

mqb2766

21

Similar to your other post about area of a triangle. You know the coordinates and one side lies along an axis so ...

Reply 2

Rhys_M

OP

11

Original post by mqb2766

Similar to your other post about area of a triangle. You know the coordinates and one side lies along an axis so ...

In my other post I didn't get an answer - you pointed out my mistake, and said now finding the area would then be simple - i don't know how to do it, we have no angles so what do i do with 3 sides?

Reply 3

mqb2766

21

What are the basic triangle area formula you know?

(edited 2 years ago)

Reply 4

Rhys_M

OP

11

Original post by mqb2766

What are the basic triangle area formula you know?

1/2bh, 1/2abSinC

Reply 5

mqb2766

21

So what is stopping you? Try the first one first.

Reply 6

Rhys_M

OP

11

Original post by mqb2766

So what is stopping you? Try the first one first.

That's just for right angled triangles so are you saying i need to split it up?
Ps: sorry for this long thread i'm really not good at geometry lol

(edited 2 years ago)

Reply 7

unplayable

10

Original post by Rhys_M

That's just for right angled triangles so are you saying i need to split it up?
Ps: sorry for this long thread i'm really not good at geometry lol

you can use 1/2bh for any triangle, you just need to make sure that your base and height are at 90 degrees to each other.

Reply 8

mqb2766

21

No it isn't.
base * perpendicular height / 2
Just try each side as the base and think do you know the perpendicular height. For this and the other problem, the perpendicular height is easy for one base/height combination.

Reply 9

Rhys_M

OP

11

Original post by mqb2766

No it isn't.
base * perpendicular height / 2
Just try each side as the base and think do you know the perpendicular height. For this and the other problem, the perpendicular height is easy for one base/height combination.

I really don't know. I get you're not supposed to give direct answers but Please can you tell me (acutally) what to use, and i'll be able to write it down and apply it to future different questions

Reply 10

mqb2766

21

If one side (base) is parallel to an axis and you know the coordinates of the other vertex, then its easy to work out the height, just using the coordinates of the vertex. In both this problem and the other problem, the base lies on an axis, and the perpendicular height is just the relevant vertex coordinate.

(edited 2 years ago)

Reply 11

Rhys_M

OP

11

Original post by mqb2766

If one side (base) is parallel to an axis and you know the coordinates of the other vertex, then its easy to work out the height, just using the coordinates of the vertex. In both this problem and the other problem, the base lies on an axis, and the perpendicular height is just the relevant vertex coordinate.

Oh so it's just 1/2 x AB x 3
Because P is 3 down from the x-axis?
The reason i thought that wouldnt work is because i thought that would include the 'missing corner bit' (to the left of P) such that a right angled triangle would be made

Thanks so much for your help - honestly you've answered so many of my questions, I need to get through the whole a-level over summer as i'm taking it a year early, and if it weren't for the volunteers like you i would be stuck

(edited 2 years ago)

Reply 12

mqb2766

21

https://www.mathsisfun.com/algebra/trig-area-triangle-without-right-angle.html

Tbh, it would be a bit of a slog, but if you knew the three sides, you could use the cos rule to get an angle and then use the absin(C)/2 formula. Similarly, Heron's formula isnt on the syllabus, but its reasonably well known
https://en.wikipedia.org/wiki/Heron%27s_formula

Reply 13

Rhys_M

OP

11

Original post by mqb2766

https://www.mathsisfun.com/algebra/trig-area-triangle-without-right-angle.html

Tbh, it would be a bit of a slog, but if you knew the three sides, you could use the cos rule to get an angle and then use the absin(C)/2 formula. Similarly, Heron's formula isnt on the syllabus, but its reasonably well known
https://en.wikipedia.org/wiki/Heron%27s_formula

Thank you so so much!
I didnt know there was an actual formula for 3 sides - will make life so much easier :smile:

Reply 14

mqb2766

21

It probably won't, but its always good to review and learn some basic geometry.

For questions like this, they want you to spot the base * perp height / 2. Its quicker to work out the area like this, than to calculate the lengths of the two sides which are not parallel to the axes.

Note the other question was 3 marks. You'd aleady found the + C y-axis intersection points, so a couple of easy lines to find the area. Nothing more is required for 3 marks.

(edited 2 years ago)

Differentiation - find triangle area question

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