Question

Blue The net of a rectangular pyramid and its dimensions are shown. What is the lateral surface area of the pyramid in square feet?

Answer 1

The opposite lateral surfaces have the same measures, so the areas of the opposide triangles will be the same.

So, we have two areas to calculate and the total lateral surface area will be the sum of two of each of these.

Let the top aand bottom triangle areas be A1 and the other two be A2. Then, the total lateral surface area will be:

`\begin{gathered} A=2A_1+2A_2_{} \\ A=2(A_1+A_2) \end{gathered}`

Notice that the rectangle is the base, so it is not included on the latera surface area.

The area of a triangle can be calculate by the product of its base and its height divided by two:

`A_(\Delta)=(b\cdot h)/(2)`

The base of the top and bottom triangles is 7.5 ft and the height is 5 ft, so A1 is:

`A_1=(7.5\cdot5)/(2)=18.75`

The base of the right and left triangles is 3.5 ft and the height is 6 ft, so A2 is:

`A_2=(3.5\cdot6)/(2)=10.5`

These areas are in ft².

Thus, the total lateral surface area is:

`\begin{gathered} A=2(A_1+A_2) \\ A=2(18.75+10.5) \\ A=2\cdot29.25 \\ A=58.5 \end{gathered}`

The total lateral surface area is 58.5 ft².