The 2005 world record for the longest sandwich is 3.6 meters with a width of 3.6 meters and a thickness of 0.44 meters. If you cut the sandwich in half diagonally, it would create a triangular prism with a hypotenuse of 5.1 meters. Apply the technique of using nets to find the surface area.

Question

(1 point)

Answer 1

To find the surface area of the triangular prism, we need to break it down into its individual shapes and calculate the area of each shape.

First, we have the two congruent triangular faces of the prism. The formula for the area of a triangle is A = 1/2 * base * height. In this case, the base and height of the triangle are 3.6 meters each. So, the area of one triangle is:

A_triangle = 1/2 * 3.6 * 3.6 = 6.48 square meters
Then, we have the three rectangular faces of the prism. Two of the rectangles have dimensions of 3.6 meters by 0.44 meters, and the other rectangle has dimensions of 5.1 meters by 0.44 meters.

The area of the two smaller rectangles is:
A_rectangle = length * width = 3.6 * 0.44 = 1.584 square meters
There are two rectangles, so the total area for these rectangles is:
2 * 1.584 = 3.168 square meters
The area of the larger rectangle is:
5.1 * 0.44 = 2.244 square meters

Finally, we add up the areas of all five faces of the triangular prism to find the total surface area:
Total Surface Area = 2(A_triangle) + 3(A_rectangle)
Total Surface Area = 2(6.48) + 3(3.168) + 2.244
Total Surface Area = 12.96 + 9.504 + 2.244
Total Surface Area = 24.708 square meters

Therefore, the total surface area of the triangular prism is 24.708 square meters.