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.
[tex]\text{Area of base}=(\text{10 in})^2=100\text{ in}^2[/tex]
Let us find area of one triangular side.
[tex]\text{Area of triangle}=\frac{1}{2}\times \text{Base}\times\text{Height}[/tex]
[tex]\text{Area of triangle}=\frac{1}{2}\times \text{10 in}\times\text{6 in}[/tex]
[tex]\text{Area of triangle}=\text{5 in}\times\text{6 in}[/tex]
[tex]\text{Area of triangle}=30\text{ in}^2[/tex]
Now we will multiply area of one triangular face by 4 to find area of 4 triangular faces.
[tex]\text{Area of 4 triangular faces}=4\times 30\text{ in}^2[/tex]
[tex]\text{Area of 4 triangular faces}=120\text{ in}^2[/tex]
Total surface area of pyramid would be area of base plus area of 4 triangular faces.
[tex]\text{Total surface area of pyramid}=100\text{ in}^2+120\text{ in}^2[/tex]
[tex]\text{Total surface area of pyramid}=220\text{ in}^2[/tex]
Therefore, 220 square inches of copper sheet are needed to make one pyramid.
