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In a quadrilateral $$ABCD$$, $$p$$, $$q$$ are the lengths of the perpendiculars drawn from the vertices $$B$$ and $$D$$ onto the diagonal $$AC$$. If $$AC = r$$, then the area of the quadrilateral $$ABCD$$ is
The diagonal $$AC$$ splits the quadrilateral into triangles $$ABC$$ and $$ADC$$ with common base $$AC = r$$ and heights $$p$$ and $$q$$. So the area is $$\frac{1}{2}rp + \frac{1}{2}rq = \frac{(p + q)r}{2}$$.
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