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 without considering contact area

The surface - area formula for a rectangular prism is $SA = 2(lw+lh + wh)$. For the lower prism with $l = 10$ cm, $w = 4$ cm, $h = 2$ cm, the total surface - area of the lower prism without considering the contact area is $SA=2(10\times4 + 10\times2+4\times2)=2(40 + 20+8)=2\times68 = 136$ $cm^{2}$.

Step2: Calculate the contact area

The contact area between the two prisms is the area of the bottom - face of the upper prism. The bottom - face of the upper prism has dimensions $3$ cm and $4$ cm, so the contact area $A = 3\times4=12$ $cm^{2}$.

Step3: Calculate the surface - area of the lower prism

The surface - area of the lower prism $SA_{lower}$ is the total surface - area of the lower prism without considering the contact area minus the contact area. So $SA_{lower}=136-12 = 124$ $cm^{2}$.

Answer:

$124$