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 each face and then add them up.
1. Calculate the area of the two triangular bases:
Area = 1/2 * base * height
Area = 1/2 * 17 inches * 10 inches
Area = 85 square inches (for each base)
2. Calculate the area of the three rectangular faces:
Area of rectangle 1 = height * length
Area of rectangle 1 = 9 inches * 10 inches
Area of rectangle 1 = 90 square inches
Area of rectangle 2 = side * length
Area of rectangle 2 = 10 inches * 10 inches
Area of rectangle 2 = 100 square inches
Area of rectangle 3 = side * length
Area of rectangle 3 = 12 inches * 9 inches
Area of rectangle 3 = 108 square inches
3. Add up the areas of all the faces:
85 + 85 + 90 + 100 + 108 = 468 square inches
Therefore, the surface area of the display showcase is 468 square inches.