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, s2s2 =12 inches, s3s3 = 17 and l =10 inches.(1 point)

Answer 1

First, let's calculate the surface area of the triangular bases:

Area of a triangle = 0.5 * base * height

Area of triangle 1 = 0.5 * 17 * 9 = 76.5 square inches
Area of triangle 2 = 0.5 * 10 * 9 = 45 square inches
Area of triangle 3 = 0.5 * 12 * 10 = 60 square inches

Next, let's calculate the surface area of the three rectangular sides:

Area of a rectangle = length * width

Area of rectangular side 1 = 17 * 10 = 170 square inches
Area of rectangular side 2 = 17 * 10 = 170 square inches
Area of rectangular side 3 = 12 * 9 = 108 square inches

Now, let's sum up the areas of all the sides:

Total surface area = 76.5 + 45 + 60 + 170 + 170 + 108
Total surface area = 629.5 square inches

Therefore, the surface area of the display showcase is 629.5 square inches.