Question

I need help finding surface area of a figure

Answer 1

The surface area will be the surface area of the rectangular prism, plus the surface area of the triangular prism, minus the area of the base of the triangular prism, so:

For the rectangular prism:

`\begin{gathered} SA_(rp)=2(lw+lh+wh) \\ where \\ l=length=4ft \\ w=width=16ft \\ h=height=6ft \\ SA_(rp)=2(4\cdot16+4\cdot6+16\cdot6) \\ SA_(rp)=2(184) \\ SA_(rp)=368ft^2 \end{gathered}`

For the triangular prism:

`\begin{gathered} SA_(tp)=2ls+bh+lb \\ where \\ l=length=4ft \\ h=height=9ft \\ b=base=12ft \\ s=side=11ft \\ SA_(tp)=2\cdot4\cdot11+12\cdot9+4\cdot12 \\ SA_(tp)=244ft^2 \end{gathered}`

The area of the base of the triangular prism is:

`A=12\cdot4=48ft^2`

Therefore:

`\begin{gathered} SA=SA_(rp)+SA_(tp)-A \\ SA=368ft^2+244ft^2-48ft^2 \\ SA=564ft^2 \end{gathered}`