Given tents have the shape of square pyramids
Length of the side of base = b
Height of the face = h
Surface area = S =
[tex]b^2+\frac{1}{2}\cdot4\cdot b\cdot h=b^2+2bh[/tex]Case (1): Tents for 2 peoples:
[tex]\begin{gathered} b=6\frac{1}{2}=\frac{13}{2}ft \\ h=5\frac{3}{5}=\frac{28}{5}ft \end{gathered}[/tex]So, the surface area =
[tex]S=(\frac{13}{2})^2+2\cdot\frac{13}{2}\cdot\frac{28}{5}=\frac{169}{4}+\frac{364}{5}=\frac{2301}{20}=115\frac{1}{20}ft^2[/tex]Case (2): Tents for 3 peoples:
[tex]\begin{gathered} b=8ft \\ S=174\frac{18}{25}ft^2=\frac{4368}{25}ft^2 \end{gathered}[/tex]We will find the height (h), So:
[tex]\begin{gathered} \frac{4368}{25}=8^2+2\cdot8\cdot h \\ \\ \frac{4368}{25}=64+16h \\ 16h=\frac{4368}{25}-64=\frac{2768}{25} \\ \\ h=\frac{2768}{25}\cdot\frac{1}{16}=\frac{173}{25}=6\frac{23}{25}ft \end{gathered}[/tex]Case (3): Tents for 4 peoples:
[tex]\begin{gathered} b=11ft \\ S=330ft^2 \\ \end{gathered}[/tex]We will find h:
[tex]\begin{gathered} 330=11^2+2\cdot11\cdot h \\ 330=121+22h \\ 22h=330-121=209 \\ \\ h=\frac{209}{22}=\frac{19}{2}=9\frac{1}{2}ft \end{gathered}[/tex]