# Find the area of the parallelogram whose vertices are listed. (0,0), (5,2), (6,4

Find the area of the parallelogram whose vertices are listed. (0,0), (5,2), (6,4), (11,6)

## Want to know more about Matrix transformations?

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

Aniqa O'Neill

Parallelogram can be described with 4 vertices or 2 vectors. Since we are given 4 vertices(ABCD), let's find vectors u, v that describe parallelogram. Graph these points to see how vectors are described
A=(0,0)
B=(5,2)
C=(6,4)
D=(11,6)
$$u=AB=\begin{bmatrix}5\\2\end{bmatrix}$$
$$u=AC=\begin{bmatrix}6\\4\end{bmatrix}$$
Area of parallelogram is absolute value of determinant
$$\begin{bmatrix}u_1 & v_1 \\u_2 &v_2 \end{bmatrix}$$
$$\begin{bmatrix}u_1 & v_1 \\u_2 &v_2 \end{bmatrix}=det\begin{bmatrix}5& 6 \\2 &4 \end{bmatrix}=20-12=8$$
Result:
8