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, 8 1 = 10 inches 8 2= 12 inches, 8 3 =17 and l =10 inches

Answer 1

To find the surface area of a triangular prism, you need to find the area of the two triangular bases and the three rectangular sides.

First, calculate the area of the triangular base:
A = 1/2 * base * height
A = 1/2 * 17 * 9
A = 1/2 * 153
A = 76.5 square inches

Since there are two triangular bases, the total area for the bases is:
2 * 76.5 = 153 square inches

Now, calculate the area of each rectangular side:
A = length * height
A(side 1) = 10 * 9 = 90 square inches
A(side 2) = 12 * 9 = 108 square inches
A(side 3) = 17 * 8 = 136 square inches

Total area for the rectangular sides:
90 + 108 + 136 = 334 square inches

Finally, add the area of the bases and the sides to get the total surface area:
153 + 334 = 487 square inches

Therefore, the surface area of the display showcase is 487 square inches.