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.(

Answer 1

To find the surface area of the triangular prism showcase, we need to calculate the area of each face and then add them all together.

1. The area of the rectangular base (b x l):
b = 17 inches, l = 10 inches
Area = 17 inches x 10 inches = 170 square inches

2. The area of the two triangular faces (1/2 x base x height):
For the first triangle:
base = s1 = 10 inches, height = h = 9 inches
Area = 0.5 x 10 inches x 9 inches = 45 square inches

For the second triangle:
base = s2 = 12 inches, height = h = 9 inches
Area = 0.5 x 12 inches x 9 inches = 54 square inches

3. The area of the three rectangular faces:
For the first rectangular face:
width = s1 = 10 inches, height = h = 9 inches
Area = 10 inches x 9 inches = 90 square inches

For the second rectangular face:
width = s2 = 12 inches, height = h = 9 inches
Area = 12 inches x 9 inches = 108 square inches

For the third rectangular face:
width = s3 = 17 inches, height = h = 9 inches
Area = 17 inches x 9 inches = 153 square inches

Now, we can sum up all the areas to find the total surface area:
170 square inches (rectangular base) + 45 square inches (first triangle) + 54 square inches (second triangle) + 90 square inches (first rectangular face) + 108 square inches (second rectangular face) + 153 square inches (third rectangular face) = 620 square inches

Therefore, the surface area of the triangular prism display showcase is 620 square inches.