# Math Help - area of a triangle with vertices

1. ## 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.
help is required please!

thanks!

2. ## Re: area of a triangle with vertices

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.

3. ## Re: area of a triangle with vertices

i don't know what the semi-perimeter rule is.

4. ## Re: area of a triangle with vertices

Hello, andyboy179!

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.)

5. ## Re: area of a triangle with vertices

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?

6. ## Re: area of a triangle with vertices

sorry i know how to do it!!! mental block!! thanks alot for the answer!!!!