Answer
The volume of the figure is \[666\text{ y}{{\text{d}}^{\text{2}}}\].
Work Step by Step
The length, width, and height of the rectangular base is \[10\text{ yd}\], \[15\text{ yd}\], and \[5\text{ yd}\], respectively.
To compute the surface area of the figure, first compute the total area of the rectangular base and second compute the surface area of the trapezoid. Finally, compute the total surface area of the figure by adding the areas of the aforesaid solid figures.
Compute the area of the rectangular base using the equation as shown below:
\[\begin{align}
& \text{Area of the rectangular base}=2\left( l+b \right)h \\
& =2\left( 10+15 \right)5 \\
& =250\text{ y}{{\text{d}}^{\text{2}}}
\end{align}\]
Compute the area of trapezoid as follows:
\[\begin{align}
& \text{Area of the trapezoid}=2\times \frac{1}{2}\left( {{b}_{1}}+{{b}_{2}} \right)h+15\times \left( \text{Sum of other sides} \right) \\
& =2\times \frac{1}{2}\left( 4\text{ yd}+10\text{ yd} \right)\times 45\text{ yd}+ \\
& \left[ 15\times \left( 5\text{ yd}+5\text{ yd}+4\text{ yd}+10\text{ yd} \right) \right] \\
& =416\text{ y}{{\text{d}}^{\text{2}}}
\end{align}\]
Now, compute the surface area of the given figure using the equation as shown below:
\[\begin{align}
& \text{Total surface area of the figure}=\text{Total surface area of the rectangular } \\
& \text{base}+\text{Surface area of the trapezoid} \\
& =\left( 250\text{ y}{{\text{d}}^{\text{2}}}+416\text{ y}{{\text{d}}^{\text{2}}} \right) \\
& =666\text{ y}{{\text{d}}^{\text{2}}}
\end{align}\]
Hence, the volume of the figure is \[666\text{ y}{{\text{d}}^{\text{2}}}\].
