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}=(1)/(2)* \text{Base}*\text{Height}`

`\text{Area of triangle}=(1)/(2)* \text{10 in}*\text{6 in}`

`\text{Area of triangle}=\text{5 in}*\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* 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.