Christian collects model cars and planes. He has a display showcase of all of his collector's 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 inches and l=10 inches
To find the surface area of a triangular prism, you must calculate the area of each face separately and then add them all together.
First, calculate the area of the two triangular bases:
Area of a triangle = 0.5 * base * height
Area of Base 1 = 0.5 * 17 inches * 10 inches = 85 square inches
Area of Base 2 = 0.5 * 12 inches * 10 inches = 60 square inches
Next, calculate the area of the three rectangular sides:
Area of the side with length 17 inches = length * height = 17 inches * 9 inches = 153 square inches
Area of the side with length 10 inches = length * height = 10 inches * 9 inches = 90 square inches
Area of the side with length 10 inches = length * side = 10 inches * 12 inches = 120 square inches
Now add all the areas together to find the total surface area of the triangular prism:
Total Surface Area = 85 sq in + 60 sq in + 153 sq in + 90 sq in + 120 sq in = 508 square inches
Therefore, the surface area of the display showcase is 508 square inches.