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 find the areas of all the individual faces and then add them together.
The formula for the surface area of a triangular prism is:
S.A. = 2*base area + lateral area
First, let's find the base area. The base of the triangular prism is a triangle with base b=17 inches and height h=9 inches. The formula for the area of a triangle is:
Area = 1/2 * base * height
Base area = 1/2 * 17 * 9 = 1/2 * 153 = 76.5 in^2
Next, let's find the lateral area. The lateral faces of a triangular prism are three rectangles with dimensions given by the three sides of the triangle. The formula for the area of a rectangle is:
Area = length * width
Lateral area = 2*(10*10 + 10*12 + 12*17) = 2*(100+120+204) = 2*(424) = 848 in^2
Now we can find the total surface area by summing the base area and lateral area:
S.A. = 2*base area + lateral area
S.A. = 2*76.5 + 848
S.A. = 153 + 848
S.A. = 1001 in^2
Therefore, the surface area of Christian's display showcase is 1001 square inches.