Question

If points A(2,2), B(4,5), and C(6,2) represents the vertices of a triangle, determine its area.
@Mertsj @satellite73 @agent0smith

Answer 1

Your name is calculusxy. Do you have to use calculus for this or just normal geometry?

Answer 2

I put calculusxy because I like to study about calculus. But this is a normal geometry question.

Answer 3

herons formula would work i think

Answer 4

Do it intuitively.
A = 1/2 * bh
b = ((Ax - Bx)^2 + (Ay - By)^2)^(1/2)
Let M be equal to the midpoint between A and B, or ((Ax+Bx)/2, (Ay+By)/2).
h = ((Mx - Cx)^2 + (My - Cy)^2)^(1/2)
A = 1/2 * (((Ax - Bx)^2 + (Ay - By)^2)((Mx - Cx)^2 + (My - Cy)^2))^(1/2)

Answer 5

I do not understand this at all :/ Can you just explain it to me in words?

Answer 6

It's kind of lengthy compared to Heron's formula, you may want to just use that. Or I could explain it.

Answer 7

do you know heron's formula? it finds the area given the lengths of the sides
you can use the distance formula to find the lengths of all three sides, then plug them in to heron's formula
i can't write it here, no latex

Answer 8

Well, i only know 1/2(b*h)

Answer 9

Okay, then just use my slightly more intuitive method.
We know that the area of a triangle is half the product of the base and height lengths (e.g., A = bh * 1/2).
The base length is the distance between A and B.
b = ((Ax - Bx)^2 + (Ay - By)^2)^(1/2)
or just:
sqrt(((Ax - Bx)^2 + (Ay - By)^2))
That is, Ax = 2, Ay = 2, Bx = 4, By = 5.
In order to find the height of triangle, we need to find the midpoint of the base. Why? Because an altitude goes from the midpoint to the top, and represents the height of the triangle. If you don't understand, draw this triangle on graph paper and draw a line from the midpoint of the base to the top vertex.
Let M be the midpoint.
M((Ax+Bx)/2, (Ay+By)/2)
Now to find the height, we take the distance between M and C.
h = ((Mx - Cx)^2 + (My - Cy)^2)^(1/2)
Now substitute b and h into the equation A = bh/2

Answer 10

Is Mx and My the midpoints of the x and the y cooridinates?

Answer 11

Sorry, also make sure the line is orthogonal to the base.

Answer 12

Yes, M(Mx, My)

Answer 13

What is orthogonal?

Answer 14

Orthogonal = perpendicular.

Answer 15

Essentially.

Answer 16

Have you tried to see where these points are?
It is a nice triangle
The area 3 x 4/2=6

Answer 17

Is your way without using the graph paper, because i need such a way?

Answer 18

Yes.

Answer 19

Just use the formula I gave you.

Answer 20

Is there any other easier way to remember the formula that you gave me? I truly found it helpful and would be happy to memorize it easily.

Answer 21

It is ridiculous. We are making of a very easy problem a very difficult one. That is not Math. Math is to to try to find the easiest way to solve a problem.

Answer 22

The way my mind works is very programmatic, and it's not a standard formula. It's not as though a geometry teacher has ever stood up and said, "Okay, everybody who wants an A has to memorize this formula." I just derived it in three seconds in my head, then wrote it down. It doesn't take much to derive.
You could, alternatively, use Heron's formula and memorize that.

Answer 23

@eliassab, it is easy. You're just caught up in the symbols. It's actually quite intuitive.

Answer 24

You do not need it.

Answer 25

Explain how you would do it, then.

Answer 26

oops it would certainly help to draw the triangle, then it would be real easy
i didn't, my mistake

Answer 27

unfortunately draw tool is not working

Answer 28

Enjoy your discussion. I am going for my morning walk in warm South Africa.

Answer 29

vacation?
http://www.wolframalpha.com/input/?i=triangle+%282%2C2%29%2C%284%2C5%29%2C%286%2C2%29

Answer 30

Wow! Thanks satellite73, you have helped me a lot. you're really great :)

Answer 31

I said 6 longtime ago

Answer 32

the picture tells it all
use one half base times height
base is the distance from (2,2) to (6,2) namely 4
height is pretty clearly 3
one half of two times three is six

Answer 33

moral of the story... draw the damned picture first!!

Answer 34

but you aren't always able to draw the picture

Answer 35

all of these ways are just the same thing in different media