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# 3d geometry

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Rectangle ABCD is the base of pyramid PABCD. If AB = 8, BC = 4, $PA \perp AD$, $PA \perp AB$, and PB = 19, then what is the volume of PABCD?

Jun 20, 2021

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First of all, ABCD has area of 32.

Knowing that P is directly above A (from PA perpendicular to AD and AB), we use the Pythagorean Theorem on triangle PAB, getting PA = $$\sqrt297$$.

With this, we have the volume of PABCD as $$\frac{32*\sqrt{297}}{3}$$, or $$32\sqrt{33}$$

Jun 20, 2021
edited by EnchantedLava68  Jun 20, 2021