Question

find the surface area of the trapezoidal prism.
$sa = \square\\ \text{in}^2$

Explanation:

Step1: Calculate area of trapezoidal bases

The formula for the area of a trapezoid is $A = \frac{(a + b)h}{2}$, where $a = 18$ in, $b = 36$ in, $h = 12$ in.
$A_{base} = \frac{(18 + 36)\times12}{2} = \frac{54\times12}{2} = 324$ in².
Since there are two bases, total area of bases is $2\times324 = 648$ in².

Step2: Calculate area of rectangular faces

• Face with dimensions 36 in and 10 in: $A_1 = 36\times10 = 360$ in².
• Face with dimensions 18 in and 10 in: $A_2 = 18\times10 = 180$ in².
• Two faces with dimensions 15 in and 10 in: $2\times(15\times10) = 2\times150 = 300$ in².

Step3: Sum all areas

Total surface area $SA = 648 + 360 + 180 + 300$.
$SA = 648 + 360 = 1008$; $1008 + 180 = 1188$; $1188 + 300 = 1488$ in².

Answer:

1488