Christian collects model cars and planes. He has a display showcase of all of 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.(1 point)
S.A.=
in.2
To find the surface area of a triangular prism, we need to calculate the area of all the faces and then add them together.
The formula for the surface area of a triangular prism is:
S.A. = 2*(base area) + (perimeter of base)*(height) + (lateral area)
First, let's calculate the base area:
Base area = 1/2 * b * h
Base area = 1/2 * 17 * 9
Base area = 1/2 * 153
Base area = 76.5 square inches
Next, let's calculate the perimeter of the base:
Perimeter = s1 + s2 + s3
Perimeter = 10 + 12 + 17
Perimeter = 39 inches
Now, let's calculate the lateral area:
Lateral area = Perimeter * height
Lateral area = 39 * 10
Lateral area = 390 square inches
Finally, let's calculate the total surface area:
S.A. = 2* (base area) + (perimeter of base)*(height) + (lateral area)
S.A. = 2*(76.5) + 39*9 + 390
S.A. = 153 + 351 + 390
S.A. = 894 square inches
Therefore, the total surface area of Christian's display showcase is 894 square inches.