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 together.
1. Calculate the area of the two triangular bases:
Area of a triangle = 1/2 * base * height
Area of base 1 = 1/2 * 10 * 17 = 85 square inches
Area of base 2 = 1/2 * 12 * 17 = 102 square inches
2. Calculate the area of the three rectangular faces:
Area of a rectangle = length * width
Area of face 1 = 10 * 9 = 90 square inches
Area of face 2 = 17 * 9 = 153 square inches
Area of face 3 = 17 * 9 = 153 square inches
3. Add up all the areas:
Total surface area = 85 + 102 + 90 + 153 + 153 = 583 square inches
Therefore, the surface area of the display showcase is 583 square inches.