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Jet001 [13]
3 years ago
15

Amy gets a new kennel for her dog. A sketch of the kennel is shown here. If the roof is in the shape of a triangular prism (bott

om face included), what is the surface area of the roof of the kennel, including the bottom face?

Mathematics
1 answer:
SpyIntel [72]3 years ago
4 0

Answer:

<em>Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2</em>

<em></em>

Step-by-step explanation:

The image is attached below

For the triangular sides of the roof, area is

A = \frac{1}{2}bh

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A =  \frac{1}{2}*4*2.24 = 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 = lh

where l 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>

<em></em>

For the bottom face, area is

A = lw

where l 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>

<em></em>

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>

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