Question

1. find the surface area of the following solid. it is composed of two right rectangular prisms.

Explanation:

Step1: Define the two prisms

Let Prism 1 be the taller left prism: dimensions $l=6$ in, $w=4$ in, $h=15$ in.
Let Prism 2 be the shorter right prism: dimensions $l=4-3=1$ in, $w=4$ in, $h=7$ in.

Step2: Calculate surface area of Prism1

Surface area formula: $2(lw + lh + wh)$

$$\begin{align*} SA_1&=2(6\times4 + 6\times15 + 4\times15)\\ &=2(24 + 90 + 60)\\ &=2(174)\\ &=348 \end{align*}$$

Step3: Calculate surface area of Prism2

$$\begin{align*} SA_2&=2(1\times4 + 1\times7 + 4\times7)\\ &=2(4 + 7 + 28)\\ &=2(39)\\ &=78 \end{align*}$$

Step4: Subtract overlapping areas

Overlap is 2 times the area of the shared face: $2\times(1\times4)=8$

Step5: Compute total surface area

Total SA = $SA_1 + SA_2 - \text{Overlap}$
$=348 + 78 - 8=458$

Answer:

$458$ square inches