Question

find the surface area of the lower prism. 10 cm 5 cm saupper = 260 cm² sa lower = ? cm² 7 cm sa total = cm² 5 cm 7 cm 13 cm remember! exclude areas where complex shapes touch.

Explanation:

Step1: Calculate surface - area of lower prism's faces

The surface - area of a rectangular prism is given by $2(lw + lh+wh)$. For the lower prism with $l = 13$ cm, $w = 7$ cm, and $h = 5$ cm, the total surface - area of the lower prism without considering the contact area is $2(13\times7 + 13\times5+7\times5)$.
$2(13\times7 + 13\times5+7\times5)=2(91 + 65 + 35)=2\times191 = 382$ $cm^{2}$.

Step2: Subtract the contact area

The contact area between the two prisms is $10\times5 = 50$ $cm^{2}$. Since we need to exclude the contact area, the surface - area of the lower prism $SA_{lower}=382-50$.
$SA_{lower}=332$ $cm^{2}$

Answer:

$332$