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)
To find the surface area of a triangular prism, we first need to calculate the area of the two triangular bases and the three rectangular sides.
The area of the two triangular bases can be calculated using the formula for the area of a triangle: A = 0.5 * base * height.
For the first base:
A1 = 0.5 * s1 * l
A1 = 0.5 * 10 * 17
A1 = 85 square inches
For the second base:
A2 = 0.5 * s2 * l
A2 = 0.5 * 12 * 17
A2 = 102 square inches
Now we calculate the area of the three rectangular sides:
S1 = b * h
S1 = 17 * 9
S1 = 153 square inches
S2 = s1 * h
S2 = 10 * 9
S2 = 90 square inches
S3 = s2 * h
S3 = 12 * 9
S3 = 108 square inches
Now, we calculate the total surface area by adding the areas of the two bases and the three sides:
Surface Area = 2(A1 + A2) + S1 + S2 + S3
Surface Area = 2(85 + 102) + 153 + 90 + 108
Surface Area = 2(187) + 153 + 90 + 108
Surface Area = 374 + 153 + 90 + 108
Surface Area = 725 square inches
Therefore, the surface area of the display showcase is 725 square inches.