Question

Find the total surface area of the trapezoidal prism in the figure.

Answer 1

The total surface area of the trapezoidal is 252 m^2

Explanation:

We calculate the surface area of a trapezoid in the following way:

The first thing is to calculate the cross-sectional area:

`\begin{gathered} A_c=(1)/(2)\cdot(a+b)\cdot h \\ a=12 \\ b=6 \\ h=8 \\ \text{replacing:} \\ A_c=(1)/(2)\cdot(12+6)\cdot8 \\ A_c=72 \end{gathered}`

Now we calculate the area of each face, just like this

`\begin{gathered} A_c=A \\ 2\cdot A=2\cdot72=144 \\ 2\cdot B=2\cdot9\cdot3=54 \\ 1\cdot C=1\cdot12\cdot3=36 \\ 1\cdot D=1\cdot6\cdot3=18 \end{gathered}`

The sums of the area of each area will be the total surface area, we calculate it like this

`\begin{gathered} A_T=144+54+36+18 \\ A_T=252 \end{gathered}`