Find an area of the triangle with the given vertices?

[veevee305]

I missed this part of class and so now cannot understand it at all. We're working with matrices right now, so it must have to do with those.

Here are the directions: Find the area of the triangle with the given vertices.

The first problem: A(0,1), B(2,6), C(5,5)

If someone could step me through this so I could do the other problems as well, it would be greatly appreciated. Thank you!

[jaybird0827]

I missed this part of class and so now cannot understand it at all. We're working with matrices right now, so it must have to do with those.

Here are the directions: Find the area of the triangle with the given vertices.

The first problem: A(0,1), B(2,6), C(5,5)

If someone could step me through this so I could do the other problems as well, it would be greatly appreciated. Thank you!

You don't need matrices to do this.

Steps:
1.) Draw a coordinate system.
2.) Plot the three points A, B, C according to the coordinate pairs given each point.
3.) Use the distance formula to find the lengths of the three sides, AB, BC, AC.
4.) If this is a right triangle, use the ordinary formula for the area of a triangle

where and are the legs of the triangle.

If this is not a right triangle, then use Hero's formula to compute the area. That formula should be in your textbook.

Now it's your turn. Please follow the preceding steps. If you get stuck, please post a reply showing how far you were able to get with the above.

[stapel_eliz]

If you have to use matrix algebra, then note that this is actually done with the determinant.

[arifjafer]

There is also one formula for finding the area of and triangle whose three vertices are given

A = 0.5 [(x₁y₃-y₁x₃) + (x₂y₁-y₂x₁) + (x₃y₂-y₃x₂)]

[stapel_eliz]

Muliply out the determinant, and compare the results with your formula....