Answer:
The surface area of the pyramid is 39 square feet.
Step-by-step explanation:
The surface area of the square is composed of 4 isosceles triangles and a square.
The area of the isosceles triangle with height [tex]h[/tex] and base length [tex]b[/tex] is given by
[tex]$A = \frac{bh}{2}$[/tex]
For the pyramid, the isosceles triangle has height [tex]h= 5ft[/tex] and base length [tex]b= 3ft[/tex]; therefore, its area is
[tex]$A = \frac{(5ft)(3ft)}{2} = 7.5ft^2$[/tex]
And therefore, the total area of the 4 triangular sides is
[tex]A_{tri}=4(7.5ft^2) =30ft^2[/tex].
The area [tex]A_{base}[/tex] of the square base of the pyramid is the square of its side length:
[tex]A_{base} =(3\:\text{ft})(3\:\text{ft}) = 9\:\text{ft}^2[/tex]
Therefore, the total surface area of the square pyramid is [tex]A_{tri}+A_{base}[/tex]:
[tex]A_{tot}= A_{tri}+A_{base} = 30ft^2+9ft^2\\[/tex]
[tex]\boxed{ A_{tot} = 39ft^2}[/tex]
Therefore, the surface area of the pyramid represented by the net is 39 square feet.
