Answer:
Explanation:
The surface area of the figure is the sum of the areas of each of the 9 faces.
Area formula
We can let b represent the edge length of the base, s represent the vertical height of a side wall, and h represent the slant height of the triangular top face.
The formula for the area of each of the 5 rectangular shapes is ...
A = LW
So their total area is ...
rectangular areas = base area + 4×sidewall area
= b² +4bs
The formula for the area of each of the triangular shapes is ...
A = 1/2bh
There are 4 of them, so their total area is ...
triangular areas = 4×(1/2bh) = 2bh
Then the surface area of the figure is ...
surface area = rectangular areas + triangular areas
SA = b² +4bs +2bh = b(b +4s +2h)
Application
Filling in the given dimensions, we find the surface area to be ...
SA = (4.5 ft)(4.5 ft + 4(6 ft) +2(3.3 ft)) = (4.5 ft)(35.1 ft)
SA = 157.95 ft² ≈ 158 ft²
The surface area of the figure is about 158 square feet.