Question

The Quick-Up Tent Company manufactures tents in the shape of square pyramids in sizes that sleep 2 people, 3 people, or 4 people. Complete questions 1-2 below. 1. Complete the table to show the specifications of each size of tent. Tent Specifications 2 People 3 People || 4 People 1 Length of Side of Base 6= ft 8 ft 11 ft 2 Height of Face 3 5 ft 5 ft ft Surface Area ft 18 174 25 ft2 330 ft?

Answer 1

Given tents have the shape of square pyramids

Length of the side of base = b

Height of the face = h

Surface area = S =

`b^2+(1)/(2)\cdot4\cdot b\cdot h=b^2+2bh`

Case (1): Tents for 2 peoples:

`\begin{gathered} b=6(1)/(2)=(13)/(2)ft \\ h=5(3)/(5)=(28)/(5)ft \end{gathered}`

So, the surface area =

`S=((13)/(2))^2+2\cdot(13)/(2)\cdot(28)/(5)=(169)/(4)+(364)/(5)=(2301)/(20)=115(1)/(20)ft^2`

Case (2): Tents for 3 peoples:

`\begin{gathered} b=8ft \\ S=174(18)/(25)ft^2=(4368)/(25)ft^2 \end{gathered}`

We will find the height (h), So:

`\begin{gathered} (4368)/(25)=8^2+2\cdot8\cdot h \\ \\ (4368)/(25)=64+16h \\ 16h=(4368)/(25)-64=(2768)/(25) \\ \\ h=(2768)/(25)\cdot(1)/(16)=(173)/(25)=6(23)/(25)ft \end{gathered}`

Case (3): Tents for 4 peoples:

`\begin{gathered} b=11ft \\ S=330ft^2 \\ \end{gathered}`

We will find h:

`\begin{gathered} 330=11^2+2\cdot11\cdot h \\ 330=121+22h \\ 22h=330-121=209 \\ \\ h=(209)/(22)=(19)/(2)=9(1)/(2)ft \end{gathered}`