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9 problems match “area of parallelogram”. Clear

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1. Area of a triangle from vectors ●○○○○ 10 ptsLet $\mathbf{a} = \begin{pmatrix} 5 \\ 1 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$. Find the area of the triangle with vertices $\mathbf{0}$, $\mathbf{a}$, and $\mathbf{b}$.
2. Side length of a parallelogram from its area ●○○○○ 10 ptsA parallelogram has adjacent sides of lengths $s$ units and $2s$ units forming a $45^\circ$ angle. The area of the parallelogram is $8\sqrt{2}$ square units. Find the value of $s$. Round to two decimal places.
3. Area of a parallelogram ●○○○○ 10 ptsIn parallelogram $ABCD$, $AB = 4$ cm, $BC = 6$ cm, and $\angle ABC = 30^\circ$. Find the area of parallelogram $ABCD$ in square centimetres.
4. Area of a parallelogram from vectors ●○○○○ 10 ptsCalculate the area of the parallelogram spanned by the vectors $\vec{a} = (3, -3, 1)$ and $\vec{b} = (4, 9, 2)$. Round to two decimal places.
5. Area of a space quadrilateral ●●○○○ 20 ptsThe points $A = (3,-4,2)$, $B = (5,-8,5)$, $C = (4,-3,0)$, and $D = (6,-7,3)$ in space form a flat quadrilateral. Find the area of this quadrilateral. Round to two decimal places.
6. Area of parallelogram from its diagonals ●●○○○ 20 ptsLet $\mathbf{p}$ and $\mathbf{q}$ be two three-dimensional unit vectors such that the angle between them is $30^\circ.$ Find the area of the parallelogram whose diagonals correspond to $\mathbf{p} + 2 \mathbf{q}$ and $2 \mathbf{p} + \mathbf{q}.$ Give your answer as a decimal.
7. Parallelogram area from sides and diagonal ●●○○○ 20 ptsTwo adjacent sides of a parallelogram are $50$ cm and $40$ cm, and one diagonal is $30$ cm. Find the area of the parallelogram in square centimetres.
8. Area of a parallelogram from vector combinations ●●○○○ 20 ptsCalculate the area of the parallelogram constructed on the vectors $\vec{a}=3\vec{p}+2\vec{q}$ and $\vec{b}=2\vec{p}-\vec{q}$, given that $|\vec{p}|=4$, $|\vec{q}|=3$ and the angle between $\vec{p}$ and $\vec{q}$ is $\frac{3\pi}{4}$. Round to two decimal places.
9. Area of a parallelogram on a log graph ●●●○○ 50 ptsGiven points $A(3,1)$ and $B\left(\frac{5}{3},2\right)$. The four vertices of parallelogram $ABCD$ all lie on the graph of $f(x)=\log_{2}\frac{ax+b}{x-1}$. Find the area of parallelogram $ABCD$. Round to two decimal places.