# area of a triangle with vertices

• Sep 23rd 2011, 06:54 AM
andyboy179
area of a triangle with vertices
hi,

i need to prove that the triangle with vertices (-2,8), (3,20) and (11,8) is isoceles. Find its area.

now for this question would i just need to draw it on a graph and dop;
BxH/2
13x12=156/2=78

if this is correct so far im unsure what to do after this point to find that it is isoceles.

thanks!
• Sep 23rd 2011, 07:06 AM
Plato
Re: area of a triangle with vertices
Quote:

Originally Posted by andyboy179
i need to prove that the triangle with vertices (-2,8), (3,20) and (11,8) is isoceles. Find its area.

You can find the length of each side.
The use the semi-perimeter rule to find the area.
• Sep 23rd 2011, 07:13 AM
andyboy179
Re: area of a triangle with vertices
i don't know what the semi-perimeter rule is.
• Sep 23rd 2011, 07:27 AM
Soroban
Re: area of a triangle with vertices
Hello, andyboy179!

Quote:

Prove that the triangle with vertices A(-2,8), B(3,20) and C(11,8) is isoceles.
Find its area.

For this question, would i just need to draw it on a graph and do:

. . $\text{Area} \:=\:\tfrac{1}{2}bh \:=\:\tfrac{1}{2}(13)(12) \:=\:78\;?$ . . . . Yes!

If this is correct so far, I;m unsure what to do after this point to find that it is isoceles.

Excellent work!
We see that $AC$ is horizontal and $AC = 13.$
And we find that the altitude from $B$ is 12.

An isosceles triangle has two equal sides.
Use the Distance Formula on side $AB.$
. . You'll find that it too is 13 units long.

(We also find that $BC$ is not 13 units long.
Hence, the triangle is not equilateral.)

• Sep 23rd 2011, 07:36 AM
andyboy179
Re: area of a triangle with vertices
Quote:

Originally Posted by Soroban
Hello, andyboy179!

Excellent work!
We see that $AC$ is horizontal and $AC = 13.$
And we find that the altitude from $B$ is 12.

An isosceles triangle has two equal sides.
Use the Distance Formula on side $AB.$
. . You'll find that it too is 13 units long.

(We also find that $BC$ is not 13 units long.
Hence, the triangle is not equilateral.)

hi, how do i use the distace formula on side AB?
• Sep 23rd 2011, 07:39 AM
andyboy179
Re: area of a triangle with vertices
sorry i know how to do it!!! mental block!! thanks alot for the answer!!!!