Answer
$V=48$ cubic centimeters
$SA=96$ square centimeters
Work Step by Step
The formula for the volume of a square-based pyramid is $V=\frac{1}{3}s^{2}h$ where $s$=length of the side and $h$=height. According to the figure, $s=6$ cm and $h=4$ cm.
$V=\frac{1}{3}s^{2}h$
$V=\frac{1}{3}(6)^{2}(4)$
$V=\frac{1}{3}(36)(4)$
$V=(12)(4)$
$V=48$ cubic centimeters
The formula for the surface area of a square-based pyramid is $SA=B+\frac{1}{2}pl$ where $B$=area of base, $p$ =perimeter of base and $l$=slant height. Using the figure, we find that:
$B=6\times6=36$
$p=4(6)=24$
$l=5$
Therefore,
$SA=B+\frac{1}{2}pl$
$SA=36+\frac{1}{2}(24)(5)$
$SA=36+12(5)$
$SA=36+60$
$SA=96$ square centimeters
