The Solution:
The correct answer is 16 square in.
Given the net in the picture on the Question section, we are asked to find the surface area of the pyramid that can form using the given net.
The pyramid (or the net) has a total of 5 surfaces, these are:
4 similar triangles, each with a base of 2 inches and a height of 3 inches; and a square of side 2 inches.
So,
The required surface area is the total area of all 5 surfaces.
By formula, the area of a triangle is
[tex]A=\frac{1}{2}bh[/tex]
While the area of a square is
[tex]A=l\times l[/tex]
So, the required area of the pyramid is
[tex]\text{Area}=4(\frac{1}{2}bh)+(l\times l)[/tex]
In this case,
[tex]\begin{gathered} =\text{base}=2\text{ in.} \\ h=\text{height}=3\text{ in.} \\ l=\text{side}=2\text{ in.} \end{gathered}[/tex]
Substituting these values in the above formula, we get
[tex]\text{Area}=4(\frac{1}{2}\times2\times3)+(2\times2)=(4\times3)+4=12+4=16in.^2[/tex]
Therefore, the correct answer is 16 square in.
