What is the surface of this square pyramid

33 ft.^2

Let’s breakdown this question:

They are asking to find the surface area of this square pyramid. The surface area is the total area of all the faces in the square pyramid. The faces are the base (which is a square) and the four triangles surrounding it.

Let’s look at the areas of all the faces.

Area of the square:
Side x Side
3 x 3
= 9

Area of one triangle:
1/2 x Base x Height
1/2 x 3 x 4
= 1/2 x 12
= 6

There are four triangular faces that make up this square pyramid.

So, area of four triangles
= 4 x (Area of one triangle)
= 4 x (6)
= 24

The total surface area of this triangular pyramid
= (Area of square) + (Area of four triangles)
= (9) + (24)
= 33 ft.^2