Question
(a) Find the area of the parallelogram with edges $v=(3,2)$ and $w=(1,4)$.(b) Find the area of the triangle with sides $v, w$, and $v+w$. Draw it.(c) Find the area of the triangle with sides $v, w$, and $w-v$. Draw it.
Step 1
In this case, the area $A$ is given by: \[A = |v \times w| = \left| \begin{array}{cc} 3 & 1 \\ 2 & 4 \end{array} \right| = |(3 \times 4) - (1 \times 2)| = |12 - 2| = |10|\] So, the area of the parallelogram is $\boxed{10}$. Show more…
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