Answer:
198 ft ^ 2
Step-by-step explanation:
The figure is divided into two, a rectangular prism and a pyramid.
The formula for the surface area for the rectangular prism is:
A1 = 2ab + 2bc + 2ac
we know that the sides are a = 4.5, b = 4.5 and c = 6, replacing:
2 * 4.5 * 4.5 + 2 * 4.5 * 6 + 2 * 4.5 * 6 = 148.5 ft ^ 2
Now for the pyramid, the surface area is:
A2 = Ab + 1/2 * p * s
The base area is, since it is a square:
Ab = 4.5 ^ 2
Ab = 20.25 ft ^ 2
Now the perimeter, being a square, is one side times 4:
p = 4.5 * 4
p = 18 ft
and the value for "s" is shown in the figure and is 3.3 ft, replacing:
A2 = 20.25 + 1/2 * 18 * 3.3
A2 = 49.95 ft ^ 2
Now the total area is:
At = A1 + A2 =
At = 148.5 + 49.95
At = 198.45 ft ^ 2
Therefore the surface area of the figure is 198 ft ^ 2
