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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

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