Question

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

Answer 1

Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2

Explanation:

The image is attached below

For the triangular sides of the roof, area is

A =
`(1)/(2)bh`

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A =
`(1)/(2)*4*2.24 =` 4.48 ft^2

for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2

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 = 30 ft^2

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 = 20 ft^2

Surface area of the roof of the dog kennel is

8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2