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
To find the surface area of a triangular prism, you need to find the areas of the two triangular bases and the three rectangular faces.
Let's start by finding the area of the two triangular bases:
Area base 1 = 0.5 * b * h
Area base 1 = 0.5 * 17 * 9
Area base 1 = 76.5 square inches
Area base 2 = 0.5 * s2 * h
Area base 2 = 0.5 * 12 * 9
Area base 2 = 54 square inches
Next, let's find the area of the three rectangular faces:
Area face 1 = s1 * l
Area face 1 = 10 * 10
Area face 1 = 100 square inches
Area face 2 = s2 * l
Area face 2 = 12 * 10
Area face 2 = 120 square inches
Area face 3 = s3 * l
Area face 3 = 17 * 10
Area face 3 = 170 square inches
Now we can find the total surface area by adding the areas of the bases and faces:
Total Surface Area = 2 * (Area base 1 + Area base 2) + Area face 1 + Area face 2 + Area face 3
Total Surface Area = 2 * (76.5 + 54) + 100 + 120 + 170
Total Surface Area = 2 * 130.5 + 390
Total Surface Area = 261 + 390
Total Surface Area = 651 square inches
Therefore, the surface area of the display showcase is 651 square inches.