# Calculating the area of a parallelogram

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?

• – Martin R Jun 9 '19 at 8:44

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 $$\sin A=\sqrt{1-\cos^2A}$$.