Heron's formula

[Haris Bin Zahid]

How to calculate the area of a triangle using Heron's formula?
I've seen it in the marking schemes and I don't quite get how it works. So I want anyone to elaborate this technique.
Saad Mughal mohdumar

 

[Saad Mughal]

I hope you understand the drawing, I'm kinda bad at this paint thing.
So, here it is. The Heron Formula, you can use it FOR ANY polygon, just remember that the (1/2) always come in the formula and the first vertice is always repeated by the end. Hope that helps!

 

[Haris Bin Zahid]

View attachment 28346
I hope you understand the drawing, I'm kinda bad at this paint thing.
So, here it is. The Heron Formula, you can use it FOR ANY polygon, just remember that the (1/2) always come in the formula and the first vertice is always repeated by the end. Hope that helps!

So any vertex can be taken as the first and last vertex?

 

[Haris Bin Zahid]

View attachment 28346
I hope you understand the drawing, I'm kinda bad at this paint thing.
So, here it is. The Heron Formula, you can use it FOR ANY polygon, just remember that the (1/2) always come in the formula and the first vertice is always repeated by the end. Hope that helps!

Thanks a lot!
Actually calculating the lengths of all the sides and perpendicular is an error-prone method. This one makes the calculation much easier.
Thanks again!

 

[Talha Irfan]

So any vertex can be taken as the first and last vertex?

NO if the polygon is ABCDEF u must go in series 1/2 (ABCDEFA) if u disorder them, u will end up wrong

 

[Saad Mughal]

So any vertex can be taken as the first and last vertex?

From what I know, No. Because, I tried this ONCE and got a wrong answer, so I always take it like ABC (A first, B second, C third).

 

[Saad Mughal]

Thanks a lot!
Actually calculating the lengths of all the sides and perpendicular is an error-prone method. This one makes the calculation much easier.
Thanks again!

You didn't really know this method?
No problem.
It's good that you asked because this is a very easy, effective method and saves a lot of time.

 

[Saad Mughal]

Oh, I just searched. This is not Heron's formula.
This is Heron's formula,
http://www.mathsisfun.com/geometry/herons-formula.html
However, whenever I find the area of a triangle, I use this method, it's the determinant method I think but it always works!

 

[Haris Bin Zahid]

You didn't really know this method?
No problem.
It's good that you asked because this is a very easy, effective method and saves a lot of time.

I did this chapter by myself, that's why I didn't know it.

 

[Haris Bin Zahid]

Oh, I just searched. This is not Heron's formula.
This is Heron's formula,
http://www.mathsisfun.com/geometry/herons-formula.html
However, whenever I find the area of a triangle, I use this method, it's the determinant method I think but it always works!

Ok.

 

[Saad Mughal]

I did this chapter by myself, that's why I didn't know it.

Oh. Good that you found out now. Practice it. It will be really really helpful, I'm sure.

 

[Haris Bin Zahid]

Oh. Good that you found out now. Practice it. It will be really really helpful, I'm sure.

I'm glad you helped. Good luck for tomorrow!

 

[Saad Mughal]

I'm glad you helped. Good luck for tomorrow!

Thanks. Same to you.

 

[Haris Bin Zahid]

Oh. Good that you found out now. Practice it. It will be really really helpful, I'm sure.

Now suppose the coordinates of a triangle are C (-2,2) A (-1,-5) and D (10,-7).
Find the area of the triangle CAD. I'm getting -37.5. Why is it negative?

 

[Saad Mughal]

Now suppose the coordinates of a triangle are C (-2,2) A (-1,-5) and D (10,-7).
Find the area of the triangle CAD. I'm getting -37.5. Why is it negative?

It's not negative. Actually, the MODULUS sign, i.e. the |...| means that the value inside, whether negative or positive will always be positive.

 

[Haris Bin Zahid]

It's not negative. Actually, the MODULUS sign, i.e. the |...| means that the value inside, whether negative or positive will always be positive.

Oh I see. I didn't realize this is modulus.
Btw I know what modulus is.

 

[Saad Mughal]

Oh I see. I didn't realize this is modulus.
Btw I know what modulus is.

Oh. Sorry for that.

 

[UFO_far_planet]

a

Now suppose the coordinates of a triangle are C (-2,2) A (-1,-5) and D (10,-7).
Find the area of the triangle CAD. I'm getting -37.5. Why is it negative?

always go anticlockwise. then area will ALWAYS be positive.

 

[Suchal Riaz]

start from ANY point but ALWAYS GO ANTICLOCKWISE

 

[Saad Mughal]

start from ANY point but ALWAYS GO ANTICLOCKWISE

What do you mean by anticlockwise? Please elaborate.