Area of a parallelogram

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.
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.
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.
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.
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.
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.

More in Quadrilaterals

Area of a trapezium Diagonals of squares and rectangles Folding paper General quadrilaterals Kites Lengths in squares and rectangles Midpoints in quadrilaterals Perimeter of a parallelogram Points inside a square Quadrilaterals from diagonals Rhombus: angles and sides Rhombus: area and diagonals Squares: midpoints and rotations Trapezium midlines and diagonals