Calculating the area of a parallelogram with only two dimensions given such its base, $b$ and diagonal lengths. Can this be done or we need another information?
$\begingroup$
$\endgroup$
-
$\begingroup$ Related: math.stackexchange.com/questions/388118/… $\endgroup$ – Martin R Jun 9 '19 at 8:44
$\begingroup$
$\endgroup$
Yes, the area of a parallelogram can be determined using the diagonal lengths $d_1,d_2$ and the base length $b$.
The expression for the area is $\frac12d_1d_2\sin A$, where $A$ is the angle between the diagonals. For calculating $\sin A$, first find $\cos A$ using the cosine formula,$$\cos A=\frac{\left(\frac{d_1}2\right)^2+\left(\frac{d_2}2\right)^2-b^2}{2\left(\frac{d_1}2\right)\left(\frac{d_1}2\right)}$$and then use the fact $\sin A=\sqrt{1-\cos^2A}$.
answered Jun 9 '19 at 9:14
