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# help 3d geo

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Rectangle ABCD is the base of pyramid PABCD. If AB=8, BC=4, PA perpendicular to AD, PA perpendicular to AB, and PB=15. Then what is the volume of PABCD?

Aug 28, 2021

#1
+12980
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Rectangle ABCD is the base of pyramid PABCD. If AB=8, BC=4, PA perpendicular to AD, PA perpendicular to AB, and PB=15. Then what is the volume of PABCD?

Hello Guest!

$$h=\overline {PA} =\sqrt{15^2-8^2}$$

$$h=\sqrt{161}$$

$$V=\frac{1}{3}\cdot \overline {AB}\cdot \overline {BC}\cdot h=\frac{1}{3}\cdot 8\cdot 4\cdot \sqrt{161}$$

$${\color{blue}V=10.\overline 6\cdot\sqrt{161}}\approx135.345$$

!

Aug 28, 2021