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Sides of a parallelogram

The sides of a parallelogram follow two important principles. The sides opposite are equal to one another and they are parallel to each other. A side can be calculated using different formulas for a parallelogram. For calculating side aa we have the followinga=p2b2a=Ahaa=hbsin(α). \begin{aligned} a &= \frac{p-2b}{2} \\[1em] a &= \frac{A}{h_a} \\[1em] a &= \frac{h_b}{\sin \left( \alpha \right)}. \end{aligned} The first formula originates from the one for the perimeter, the second formula from the one for the area and the last formula from the one for the height. The formulas for the other side bb are symmetric to the ones for the side aa, i.e.b=p2a2b=Ahbb=hasin(β). \begin{aligned} b &= \frac{p-2a}{2} \\[1em] b &= \frac{A}{h_b} \\[1em] b &= \frac{h_a}{\sin \left( \beta \right)}. \end{aligned}