Question

1 ft
14 in
18 in
surface area = _____________
10.3 ft
7.1 ft
8.5 ft
surface area = _____________

Explanation:

First Rectangular Prism (with mixed units)

Step1: Convert 1 ft to inches

Since 1 ft = 12 in, the dimensions are \( l = 18 \) in, \( w = 14 \) in, \( h = 12 \) in.

Step2: Use surface area formula for rectangular prism \( SA = 2(lw + lh + wh) \)

\[

$$\begin{align*} SA &= 2((18\times14)+(18\times12)+(14\times12))\\ &= 2(252 + 216 + 168)\\ &= 2(636)\\ &= 1272 \end{align*}$$

\]

Second Rectangular Prism (all in feet)

Step1: Identify dimensions \( l = 8.5 \) ft, \( w = 7.1 \) ft, \( h = 10.3 \) ft

Step2: Apply surface area formula \( SA = 2(lw + lh + wh) \)

\[

$$\begin{align*} SA &= 2((8.5\times7.1)+(8.5\times10.3)+(7.1\times10.3))\\ &= 2(60.35 + 87.55 + 73.13)\\ &= 2(221.03)\\ &= 442.06 \end{align*}$$

\]

Answer:

First prism surface area: \( 1272 \) square inches
Second prism surface area: \( 442.06 \) square feet