Answer:
[tex]39\text{ inch}^2[/tex]
Step-by-step explanation:
We have been given diagrams of a pyramid and its net are shown. We are asked to find the surface area of our given pyramid.
The surface area of our pyramid would be equal to the area of all faces of the given net of pyramid.
We can see that our given net consists 4 triangles ans one base square.
[tex]\text{Area of triangle}=\frac{1}{2}\times b\times h[/tex], where,
b = Base of triangle,
h = Height of triangle.
[tex]\text{Area of 4 triangles}=4\times \frac{1}{2}\times 3\text { in} \times 5\text { in}[/tex]
[tex]\text{Area of 4 triangles}=2\times 3\text { in}\times 5\text { in}[/tex]
[tex]\text{Area of 4 triangles}=30\text { in}^2[/tex]
[tex]\text{Area of square}=a^2[/tex], where,
a = Each side of square.
[tex]\text{Area of square}=(3\text { in})^2[/tex]
[tex]\text{Area of square}=9\text { in}^2[/tex]
[tex]\text{Total surface area of pyramid}=30\text{ inch}^2+9\text{ inch}^2[/tex]
[tex]\text{Total surface area of pyramid}=39\text{ inch}^2[/tex]
Therefore, the total surface area of the given pyramid would be 39 square inches.
