Question

find the area of the triangle with vertices at (2,3,5) ,Q(4,2,1),R(3,6,4)

Answer 1

This one is quite long. I might have to do it on paper.

Answer 2

use draw

Answer 3

P(2, 3, 5)
Q(4, 2, 1)
R(3, 6, 1)

\[a = PQ = \sqrt{(4-2)^{2} + (2 - 3)^{2} + (1 - 5)^{2}} \]
\[= \sqrt{2^{2} + (-1)^{2} + (-4)^{2}}\]
\[= \sqrt{21}\]

\[b = QR = \sqrt{(3-4)^{2} + (6-2)^{2} + (1 - 1)^{2}}\]
\[\sqrt{(-1)^{2} + 4^{2}+ 0}\]
\[\sqrt{?}\]

\[c = RP = \sqrt{(2-3)^{2} + (6-3)^{2} + (1-5)^{2}}\]
\[= \sqrt{(-1)^{2} + 3^{2} + (-4)^{?}}\]
\[= \sqrt{26}\]

Now you just need to convert from surds using Heron's formula and it's a cakewalk from there.

Answer 4

\[b = QR = \sqrt{17}\]

Answer 5

Let me know if you get stuck with the rest of the question and I'll walk you through it.

Answer 6

but remember that area=1/2bh

Answer 7

am talking about area of the triangle not vector

Answer 8

There are different ways you can do this. My method is to find the length of each side, convert them to decimal, then use Heron's formula to find the area.

Answer 9

You could also take the cross product of two of the points, then define the origin and work from that.

Answer 10

please use the second method and let me see. Thanks

Answer 11

go further by using the heron formular

Answer 12

Firstly:

\[a = \sqrt{21} = 4.583\]

\[b = \sqrt{17} = 4.123\]

\[c = \sqrt{26} = 5.099\]
Heron's formula is denoted as

\[A = \sqrt{(s(s-a)(s-b)(s-c))}\]

where

\[s = (a+b+c)/2\]

Calculate s using the above equation, then use the area equation to find the area of the triangle.

Answer 13

http://mathworld.wolfram.com/TriangleArea.html

Answer 14

I am not sure if this form of Heron's formula works in 3 dimensions, since the 3D version of Pythagorean theprem is different http://www.jstor.org/discover/10.2307/3619577?uid=3738256&uid=2129&uid=2&uid=70&uid=4&sid=47698963103007

Answer 15

That's for a pyramid with 4 vertices, this is for a triangle lying inside a 3D plane.

Answer 16

i got A has 80.30

Answer 17

what is the formular for area

Answer 18

can i do it this way