Question

Use the given lateral area and the diagram to find the missing measure of the solid. Then, find the surface area. Round to the nearest tenth if necessary

Answer 1

The formula for the lateral surface area (LSA) is,

`LSA=2(lh+wh)=2h(l+w)`

Given:

`\begin{gathered} l=5in,w=1in,h=? \\ LSA=48in^2 \end{gathered}`

Therefore,

`\begin{gathered} 48=2h(5+1) \\ 48=2h(6) \end{gathered}`

Evaluate for h

`\begin{gathered} 48=12h \\ Divide\text{ both sides by 12} \\ (48)/(12)=(12h)/(12) \\ 4=h \\ \Rightarrow h=4 \end{gathered}`

Let us now solve for the Total surface area (TSA)

The formula for TSA is,

`TSA=2(lw+wh+hl)`

Therefore,

`\begin{gathered} TSA=2(5*1+1*4+4*5)=2(5+4+20)=2(29)=58 \\ \therefore TSA=58in^2 \end{gathered}`

Hence,

`\begin{equation*} TSA=58in^2 \end{equation*}`