Question

Look at this prism and its net. Rectangular prism with length labeled 5 meters, width labeled 7 meters, and height labeled 12 meters. Net of the same rectangular prism with the same dimensionsn labeled. What is the surface area of this rectangular prism?

Answer 1

There will be three pairs of matching sides: one pair 5x7, one pair 5x12 and one pair 12x7. We can compute the are of each side (in pairs) and then add up the total:

$A_{surf}=2\times(l \times w)+2\times(l \times h)+2\times(h \times w)$
$A_{surf}=2\times(5\times7)+2\times(5\times12)+2\times(12\times7)$
$A_{surf}=2\times35+2\times60+2\times84$
$A_{surf}=70+120+168$
$A_{surf}=358$ 
$A_{surf}=358m^{2}$