Question

shauns tent (shown below) is a triangular prism.
find the surface area, including the floor, of his tent.
\boxed{} \text{ m}^2

Explanation:

Step1: Calculate the area of the triangular faces

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of each triangular face is \(b = 1.5+1.5=3\) m and the height \(h = 2.6\) m.

$$A_{triangle}=\frac{1}{2}\times3\times2.6 = 3.9$$

Since there are \(2\) triangular faces, \(A_{triangles}=2\times3.9 = 7.8\)

Step2: Calculate the area of the rectangular faces

There are \(3\) rectangular faces.

• Two rectangles have dimensions \(3\times5\) (the non - floor rectangles). \(A_{non - floor\ rectangles}=2\times(3\times5)=30\)
• One rectangle (the floor) has dimensions \((1.5 + 1.5)\times5=3\times5 = 15\)

Step3: Calculate the total surface area

$$A_{total}=A_{triangles}+A_{non - floor\ rectangles}+A_{floor}$$

$$A_{total}=7.8+30 + 15$$

$$A_{total}=52.8$$

Answer:

\(52.8\)