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natali 33 [55]
3 years ago
9

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 $PABCD$?
Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
8 0

Answer:

<h2>181.33</h2>

Step-by-step explanation:

Since the base of the pyramid PABCD is a rectangle, the shape in question is a rectangular based pyramid. Volume of a rectangular based pyramid is expressed as V = 1/3 * Base Area * Height of the pyramid.

Given a rectangle ABCD with AB = 8 and BC = 4, the area of the rectangle will be equivalent to the base area of the pyramid.

Base Area = Length * Breadth

Base Area = AB * BC

Base Area = 8*4 = 32

If \overline{PA}\perp \overline{AD}\ and \ \overline{PA}\perp \overline{AB}, and PB = 17, then the height of the pyramid is PB = 17.

Volume of the pyramid = 1/3 * 32 * 17

Volume of the pyramid = 1/3 * 544

Volume of the rectangular based pyramid = 181.33

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