# Thread: Area of a triangle

1. ## Area of a triangle

Use calculus to determine the area of the triangle give the verticies

(0,5) (2,-2) (5,-1)

2. Originally Posted by treetheta
Use calculus to determine the area of the triangle give the verticies

(0,5) (2,-2) (5,-1)
use calculus? what class are you in? there are many simple geometric ways to do this. i can't think of any real calculus ways, unless you want to use vectors or something

3. We have to use Integrals, and it's First year calculus course

if you don't mind can you show me the vectors way as well

4. Originally Posted by treetheta
We have to use Integrals, and it's First year calculus course

if you don't mind can you show me the vectors way as well
oh, ok, duh!

have you drawn the triangle? do you see what functions it is bounded by? they will be straight lines

you will need two integrals

5. Yah I have, I just don't get how to integrate with the equation's like from what to what

I know I should be using the intersects but there's 3 intersects and I think I only need to use 2 of them

6. Originally Posted by treetheta
Yah I have, I just don't get how to integrate with the equation's like from what to what

I know I should be using the intersects but there's 3 intersects and I think I only need to use 2 of them
see the pick below. the desired area is given by $\displaystyle A = \int_0^2 [f(x) - g(x)]~dx + \int_2^5 [f(x) - h(x)]~dx$. i leave it to you to find $\displaystyle f(x) ,~g(x) \text{, and }h(x)$

7. Yah see I knew I had to do 2 integrals

how did you know it had to be from 0,2 and 2,5

8. Originally Posted by treetheta
Yah see I knew I had to do 2 integrals

how did you know it had to be from 0,2 and 2,5
recall that we find area of a bounded region by integrating the top function minus the bottom function. f(x) is always on top, but g(x) is the bottom function between x = 0 and x = 2. similarly, h(x) is the bottom function from 2 to 5. the points we were given are our guides.

9. You are one smart cookie (: