+26367 NVM. Answer is 160.
Rectangle ABCD is the base of pyramid PABCD.
If AB = 8, BC = 4,\(\overline{PA}\perp \overline{AD}\), \( \overline{PA}\perp \overline{AB}\), and PB = 17,
then what is the volume of PABCD?
Let h = height of the pyramid
Let B = Area of the Base of the pyramid = Area of the rectangle ABCD = \(4\cdot 8\) = \(32\)
\(\mathbf{h=\ ? }\)
\(\begin{array}{|rcll|} \hline h^2 + AB^2 &=& PB^2 \\ h^2 + 8^2 &=& 17^2 \\ h^2 &=& 17^2-8^2 \\ h^2 &=& 289-64 \\ h^2 &=& 225 \\ \mathbf{h} & \mathbf{=}& \mathbf{15} \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline \text{Volume of PABCD} &=& \dfrac{1}{3}\cdot B \cdot h \\\\ &=& \dfrac{1}{3}\cdot 32 \cdot 15 \\\\ &=& 5\cdot 32 \\\\ \mathbf{\text{Volume of PABCD}} & \mathbf{=}& \mathbf{160} \\ \hline \end{array}\)
