# Fnd the area A of the triangle with the given the vertices

• I
• Medtner
In summary, the conversation discusses finding the slopes and equations for three lines given specific coordinate points. The conversation also includes calculating the integral for the given lines, but the answer obtained is incorrect. The error is found in the calculation of the y-intercept for the line between (1,8) and (3,5), which should be 19/2 instead of 19. It is suggested to use coordinate geometry or the Shoelace formula to find the area of the triangle instead of using calculus.
Medtner
(0, 0), (3, 5), (1, 8)

Find the slopes and equations for each line

(0,0) ----> (3,5) = 5/3x
(0,0)---->(1,8) = 8x
(1,8)---->(3,5) = -3/2x+ 19

Then I set up the integrals (on x)

Integral sign from 0 to 1 (8x-5/3x)dx + Integral sign from 1 to 3 [(-3/2x+19)-5/3x) dx

I got 117/4 as an answer and that's wrong. My algebra/arithmetic isn't wrong (i triple checked it) so it must have something to do with the set up. What's wrong with it?

Last edited:
For the line specified by (1,8) and (3,5), what algebra/arithmetic did you use to get a y-intercept of 19?

that should be

(0,0) ----> (3,5) = 5/3x
(0,0)---->(1,8) = 8x
(1,8)---->(3,5) = -3/2x+ 19/2

I suppose the directions asked for an integral it is not the best way otherwise

lewando said:
For the line specified by (1,8) and (3,5), what algebra/arithmetic did you use to get a y-intercept of 19?
3+8*2=19
then divide by 2

Wait, 19/2?

y=mx+b
For the slope i got (-3/2)
used point (3,5)
5=-3/2(3)+b
10=-9
19=b

Did I do something wrong?

should be
Medtner said:
Wait, 19/2?

y=mx+b
For the slope i got (-3/2)
used point (3,5)
5=-3/2(3)+b
10=-9+2b
19=2b
b=19/2

Did I do something wrong?

Where did you get the 2b from?

when you multiply both sides by 2 also multiply b

Have you been specifically told to use calculus for this problem ?

If not then the area of the triangle can be calculated directly from the vertex coordinates .

Try searching on ' finding area of a triangle using coordinate geometry '

and for general interest ' Shoelace formula '

If this is homework then it should really be in the PF homework section .

## 1. How do I find the area of a triangle with given vertices?

To find the area of a triangle with given vertices, you can use the formula A = 1/2 * base * height. The base and height can be calculated by finding the difference between the x-coordinates and y-coordinates of the vertices, respectively.

## 2. Can I use the Pythagorean Theorem to find the area of a triangle?

No, the Pythagorean Theorem is used to find the length of the sides of a right triangle, not the area. To find the area of a triangle, you need to use the formula A = 1/2 * base * height.

## 3. What if the vertices of the triangle are not given in a specific order?

The order of the vertices does not matter in finding the area of a triangle. You can still use the formula A = 1/2 * base * height, as long as you use the correct values for the base and height.

## 4. Do I need to know the coordinates of all three vertices to find the area?

Yes, you need to know the coordinates of all three vertices in order to accurately find the area of a triangle. Without all three vertices, you may not have enough information to calculate the base and height.

## 5. Is there another formula I can use to find the area of a triangle?

Yes, there is another formula you can use to find the area of a triangle with given vertices. It is called Heron's formula and it uses the lengths of the sides of the triangle to calculate the area. However, using the formula A = 1/2 * base * height is typically easier and more straightforward.

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