Question

find the surface area of the lower prism. saupper = 101 cm² salower = ? cm² satotal = cm² remember! exclude areas where complex shapes touch.

Explanation:

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

The lower prism has dimensions: length $l = 10$ cm, width $w = 4$ cm, height $h = 2$ cm.
The bottom face area $A_{bottom}=l\times w=10\times4 = 40$ $cm^{2}$.
The two side - faces areas: $2\times(w\times h)=2\times(4\times2)=16$ $cm^{2}$.
The two end - faces areas: $2\times(l\times h)=2\times(10\times2)=40$ $cm^{2}$.
The area of the top face of the lower prism that is in contact with the upper prism is not part of the surface - area. But we need to account for the area that is exposed around the contact. The contact area is $3\times4 = 12$ $cm^{2}$. The exposed part of the top face of the lower prism is $(10\times4-3\times4)=(40 - 12)=28$ $cm^{2}$.

Step2: Sum up the surface - areas of the faces

$SA_{lower}=40+16 + 40+28$
$SA_{lower}=124$ $cm^{2}$

Answer:

$124$