"Find the area of the parallelogram with vertices..." was answered by our community

Reeves

Answered question

2021-05-13

Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1)

Cristiano Sears

Skilled2021-05-14Added 96 answers

See the answer below:

Jeffrey Jordon

Expert2021-09-29Added 2605 answers

Vertices are $A (- 3, 0), B (- 1, 6), C (8, 5)$ and $D (6, - 1)$

$\vec{A B} =< - 1 - (- 3), 6 - 0 >=< 2, 6 >$

$\vec{A D} =< 6 - (- 3), - 1 - 0 >=< 9, - 1 >$

Hence area of parallelogram

$= | \vec{A B} \times \vec{A D} |$

$\vec{A B} \times \vec{A D} = [\begin{matrix} i & j & k \\ 2 & 6 & 0 \\ 9 & - 1 & 0 \end{matrix}]$

$= i (0 - 0) + j (0 - 0) + k (- 2 - 54)$

$= - 56 k$

Hence

Area $= | \vec{A B} \times \vec{A D} |$

$= \sqrt{(- 56)^{2}} = 56$

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