Question

A home builder wants to decorate the post at the bottom of a stairway. One way to do this is to glue a square-based pyramid to the top of the post. The pyramid is made from a single, folded sheet of copper. The square is 10 inches on a side, and the triangular sides have a central height of 6 inches.
How many square inches of copper sheet are needed to make on pyramid?

Answer 1

We have been given net of a pyramid. We are asked to find the total surface area of the pyramid.

The surface area of the pyramid will be area of base plus area of 4 triangular sides.

We have been given that base of pyramid is square, so area of base will be square of base side.

$\text{Area of base}=(\text{10 in})^2=100\text{ in}^2$

Let us find area of one triangular side.

$\text{Area of triangle}=\frac{1}{2}\times \text{Base}\times\text{Height}$

$\text{Area of triangle}=\frac{1}{2}\times \text{10 in}\times\text{6 in}$

$\text{Area of triangle}=\text{5 in}\times\text{6 in}$

$\text{Area of triangle}=30\text{ in}^2$

Now we will multiply area of one triangular face by 4 to find area of 4 triangular faces.

$\text{Area of 4 triangular faces}=4\times 30\text{ in}^2$

$\text{Area of 4 triangular faces}=120\text{ in}^2$

Total surface area of pyramid would be area of base plus area of 4 triangular faces.

$\text{Total surface area of pyramid}=100\text{ in}^2+120\text{ in}^2$

$\text{Total surface area of pyramid}=220\text{ in}^2$

Therefore, 220 square inches of copper sheet are needed to make one pyramid.