$\begin{array}{rl}A=& l\times w\end{array}$

$\begin{array}{rl}A=& 8\times \mathrm{12}\end{array}$

$A=96 m^2$

$\begin{array}{rl}A=& l\times w\end{array}$

$\begin{array}{rl}A=& 8\times 6\end{array}$

$A=48 m^2$

Since there are two faces (front and back), we will multiply by 2:

$A=48\times 2$

$A=96 m^2$

$\begin{array}{rl}A=& l\times w\end{array}$

$\begin{array}{rl}A=& 6\times \mathrm{12}\end{array}$

$A=72 m^2$

Since there are two sides, we will multiply by 2:

$A=72\times 2$

$A=144 m^2$

To calculate the total surface area, add up the totals for each part altogether.

$\begin{array}{rl}A=& \mathrm{96}+\mathrm{96}+\mathrm{144}\end{array}$

$A=336 m^2$

$A=\frac{1}{2}\mathrm{base}\times \mathrm{height}$

$A=\frac{1}{2}\left(8\times 3\right)$

$A=\frac{1}{2}\left(\mathrm{24}\right)$

$A=12 m^2$

Since there are two faces, we will multiply by 2:

$\begin{array}{rl}A=& \mathrm{12}\times 2\end{array}$

$A=24 m^2$

To calculate surface area of the two side faces of the triangular prism, we need to know the measurement of the other sides of the triangular base.

Note: The side’s length measures 5 metres.

$\begin{array}{rl}A=& l\times w\end{array}$

$\begin{array}{rl}A=& 5\times \mathrm{12}\end{array}$

$A=60 m^2$

Since there are two sides, we will multiply by 2:

$\begin{array}{rl}A=& \mathrm{60}\times 2\end{array}$

$A=120 m^2$

To calculate the total surface area, add up the totals for each part altogether.

$\begin{array}{rl}A=& \mathrm{24}+\mathrm{120}\end{array}$

$A=144 m^2$

1. What is the formula for calculating the surface area of a cylinder?

$A=$ area of base (circle) $+$ area of base (circle) $+$ circumference of the circle $\times$ height of the cylinder.

$A=\pi r^2+\pi r^2+2\pi rh$

2. What is the formula for calculating the surface area of a rectangular prism?

$A=$ (2 area of the side face) $+$ (2 area of the front face) $+$ (2 area of the bottom face)

To calculate the total surface area, add up the totals for each part altogether.

$A=265.40 m^2$

1. What is the formula for calculating the volume of a rectangular prism?

$V=$ area of the base $\times$ the height

$V=(8\times 6)\times 12$

$V=576m^2$

2. What is the formula for calculating the volume of a triangular prism?

$V=\frac{1}{2}$ (base of the triangle) $\times$ height of the triangle $\times$ length of the prism

$V=\frac{1}{2}(8\times 3\times 12)$

$V=144m^3$

3. What is the total volume of the three-dimensional composite object?

Now that we have calculated the volume of each composite object, we can add their volumes altogether to get the total:

$V=\mathrm{576}+\mathrm{144}$

$V=720 m^3$

Therefore, the total volume area of the house is $\mathrm{720}{m}^3$.