Question

Christian collects model cars and planes. he has a display showcase of all his collectors' items. Solve this real - world problem to find the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions: h=9 inches, b=17 inches, s1=10 inches, s2= 12 inches, s3=17 and l=10 inches.

S.A.=___ in.^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of a triangular prism, you need to find the area of all the individual faces and then add them together.

The formula for the surface area of a triangular prism is:
S.A. = 2(Abase) + (Pperimeter)(h)

Where Pperimeter is the perimeter of the base and h is the height of the prism.

First, find the area of the two triangular bases:
Abase = (1/2)bh
Abase = (1/2)(17)(10)
Abase = 85 in^2

Now, find the perimeter of the base (Pperimeter):
Pperimeter = s1 + s2 + s3
Pperimeter = 10 + 12 + 17
Pperimeter = 39 in

Now, find the surface area of the two triangular bases and the side faces:
S.A. = 2(85) + (39)(9)
S.A. = 170 + 351
S.A. = 521 in^2

Therefore, the surface area of the display showcase is 521 square inches.