# Thread: Finding an area using matrices & determinants

1. ## Finding an area using matrices & determinants

Find the area of the triangle with vertices, $\displaystyle (1,3)$, $\displaystyle (2,7)$ and $\displaystyle (4,1)$.

I went about this by drawing a diagram and then forming a rectangle containing the area described above, and 3 other triangles, calculated the area of these and subtracted it to find the area in the question, 7.

However looking at the answers it appears as if we were meant to do this using matrices and determinants.

Here's what the solutions say:

Area $\displaystyle = \frac{1}{2}det(A)$ where $\displaystyle A = \begin{pmatrix} 1&1&3 \\ 1&2&7 \\ 1&4&1 \end{pmatrix}$.

Now I gather that the last two columns are the coordinates of the vertices, just unsure where the 1s in the first column come from.

Thanks in advance

2. add addition dimension to form 3D shape by triangle as bottom, height is 1,
So Volume = 2 * Area of Triangle * Height = det(...)

3. Thank you