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Sagot :
The surface area of the pyramid is 60 square feet
The surface area of the square prism is 480 square feet
The surface area of the cube is 180 square feet
The total surface area is 720 square feet
Area of Composite figures
From the question, we are to calculate the surface area of each part of the composite figure
- For the cube
Surface area of a cube is given by
[tex]S = 6l^{2}[/tex]
Where [tex]l[/tex] is the length of a side
But only have 5 surfaces of the cube are part of the composite figure
∴ Surface area of the cubic part of the figure = [tex]5l^{2}[/tex]
From the given information,
[tex]l = 6 \ feet[/tex]
∴ Surface area of the cubic part of the figure = 5 × 6²
Surface area of the cubic part of the figure= 180 square feet
- For the square prism
The surface area of a square prism is given by the formula,
[tex]S = 2l^{2} + 4lh[/tex]
Where [tex]l[/tex] is the length of the sides and
[tex]h[/tex] is the height
But the square surfaces are not part of the surface of the figure
∴ Surface area of the square prism in the figure = [tex]2l^{2} + 4lh - 2l^{2}[/tex]
Surface area of the square prism in the figure = [tex]4lh[/tex]
From the given information,
[tex]l = 6 \ feet[/tex]
[tex]h = 20 \ feet[/tex]
Thus,
Surface area of the square prism part of the figure = 4×6×20
Surface area of the square prism part of the figure = 480 square feet
- For the pyramid
The pyramid is a square pyramid
The surface area of a square pyramid is given by
[tex]S = l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h ^{2} }[/tex]
Where [tex]l[/tex] is the base length
and [tex]h[/tex] is the height of the prism
But the square base is not part of the surface of the figure
∴ Surface area of the pyramid part of the figure = [tex]l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h^{2} }\ - ( l^{2})[/tex]
Surface area of the pyramid part of the figure = [tex]2l\sqrt{\frac{l^{2} }{4}+h^{2} }[/tex]
From the given information,
[tex]l = 6 \ feet[/tex]
[tex]h = 4 \ feet[/tex]
∴ Surface area of the pyramid part of the figure = [tex]2(6)\sqrt{\frac{6^{2} }{4}+4^{2} }[/tex]
= [tex]12\sqrt{\frac{36 }{4}+16}[/tex]
= [tex]12\sqrt{9+16 }[/tex]
= [tex]12\sqrt{25}[/tex]
= 12 × 5
= 60 square feet
Hence, the surface area of the pyramid is 60 square feet
Thus,
The total surface area = 180 square feet + 480 square feet + 60 square feet
The total surface area = 720 square feet
Hence, the total surface area is 720 square feet
Learn more on Calculating area of composite figures here: https://brainly.com/question/13175744
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