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 si…

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asked Dec 27, 2021 122k views

1 Answer

Jcal · Answer 1 · 2022-01-03T02:12:28+0000

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.