Question

(10) How much material is required to make a tent with the following dimensions? (Hint: Prisms are named for the shape of their bases.) 2 m 2.5 m 2.25 m 2.5 m

Answer 1

In order to calculate how much material is required to make this tent, we need to calculate its surface area.

To do so, let's calculate the area of each face of this triangular prism:

- Two triangles with base = 2.5 and height = 2

- Three rectangles with dimensions 2.25 m and 2.5 m.

The area of each triangle is:

`\begin{gathered} A_1=(b\cdot h)/(2) \\ A_1=(2.5\cdot2)/(2)=2.5 \end{gathered}`

The area of each rectangle is:

`\begin{gathered} A_2=l\cdot w \\ A_2=2.25\cdot2.5 \\ A_2=5.625 \end{gathered}`

Now, calculating the surface area, we have:

`\begin{gathered} S=2\cdot A_1+3\cdot A_2 \\ S=2\cdot2.5+3\cdot5.625 \\ S=5+16.875 \\ S=21.875 \end{gathered}`

So the amount of material needed is 21.875 m²