What is the surface area of the square pyramid represented by the net?

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 and base length is given by

For the pyramid, the isosceles triangle has height and base length ; therefore, its area is

And therefore, the total area of the 4 triangular sides is

.

The area  of the square base of the pyramid is the square of its side length:

Therefore, the total surface area of the square pyramid is :

Therefore, the surface area of the pyramid represented by the net is 39 square feet.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1