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Answer:
<em>Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2</em>
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Step-by-step explanation:
The image is attached below
For the triangular sides of the roof, area is
A =
where b is the base = 4 ft
h is the vertical height = 2.24 ft
A = 4.48 ft^2
for the two faces we have 2 x 4.48 ft^2 = <em>8.96 ft^2</em>
For the rectangular sections of the roof, area is
A =
where is the length of the rectangle = 5 ft
h is the height of the rectangle = 3 ft
A = 5 x 3 = 15 ft^2
For the two rectangular faces, we have 2 x 15 ft^2 = <em>30 ft^2</em>
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For the bottom face, area is
A =
where is the length of the house = 5 ft
w is the width of the house = 4 ft
A = 5 x 4 = <em>20 ft^2</em>
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Surface area of the roof of the dog kennel is
<em>8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2</em>
A
The volume (V) of a pyramid is found using the formula
V = × area of base × height(h)
area of base = 9² = 81 ← area of a square, hence
324 = × 81 × h = 27h ( divide both sides by 27 )
h = = 12 → A