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
2
=12 inches, s3
3
= 17 and l=10 inches.(1 point)
S.A.= in.2
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To find the surface area of a triangular prism, we need to add the areas of all the individual faces.
The formula for the surface area of a triangular prism is:
S.A = (2 * base area) + (perimeter of base * height) + (2 * side area)
First, let's find the base area of the triangular prism:
Base area = (1/2) * base * height
Base area = (1/2) * 17 * 9
Base area = 76.5 square inches
Next, let's find the perimeter of the triangular base:
Perimeter = s1 + s2 + s3
Perimeter = 10 + 12 + 17
Perimeter = 39 inches
Now, let's find the side area of the triangular prism:
Side area = l * height
Side area = 10 * 9
Side area = 90 square inches
Now, calculate the surface area:
S.A. = (2 * 76.5) + (39 * 9) + (2 * 90)
S.A. = 153 + 351 + 180
S.A. = 684 square inches
Therefore, the surface area of the display showcase is 684 square inches.
I apologize for the error in my previous calculation. Let's correct it.
The surface area of a triangular prism is the sum of the areas of all its faces.
First, let's find the area of the triangular base:
Base area = (1/2) * base * height
Base area = (1/2) * 17 * 9
Base area = 76.5 square inches
Next, let's find the area of the two triangular faces:
Side areas = 2 * (1/2) * base * height
Side areas = 2 * (1/2) * 10 * 9
Side areas = 90 square inches
Now, let's find the area of the three rectangular faces:
Rectangle 1 area = base * height
Rectangle 1 area = 17 * 9
Rectangle 1 area = 153 square inches
Rectangle 2 area = side1 * height
Rectangle 2 area = 10 * 9
Rectangle 2 area = 90 square inches
Rectangle 3 area = side2 * height
Rectangle 3 area = 12 * 9
Rectangle 3 area = 108 square inches
Now, let's sum up the areas of all the faces:
Total surface area = 76.5 + 90 + 90 + 153 + 90 + 108
Total surface area = 607.5 square inches
Therefore, the correct surface area of the display showcase is 607.5 square inches. Thank you for bringing the error to my attention.