What is the total surface area represented by this net of a triangular prism that is 9cm, 17cm, 7.8 cm, 17cm, 9, 17cm and 9cm

To find the total surface area of the triangular prism, we need to calculate the areas of each of the surfaces:

1. Base triangles: The base of the triangular prism is an isosceles triangle with side lengths of 9 cm, 17 cm, and 17 cm. We can calculate the area of one base triangle using the formula for the area of a triangle: (1/2) * base * height. In this case, the base is 9 cm and the height can be calculated using the Pythagorean theorem:
height = sqrt(17^2 - (9/2)^2) = √(289 - 40.5) = √248.5 ≈ 15.77 cm

Area of one base triangle = (1/2) * 9 * 15.77 ≈ 70.97 cm^2

Since there are two base triangles, the total area of the base is 2 * 70.97 = 141.94 cm^2.

2. Rectangular faces: There are three rectangular faces on a triangular prism. Two of the faces are rectangles with dimensions 9 cm by 17 cm, and the third face is a rectangle with dimensions 17 cm by 7.8 cm.

Area of the first two rectangles = 2 * 9 * 17 = 306 cm^2
Area of the third rectangle = 17 * 7.8 = 132.6 cm^2

Total area of the rectangular faces = 306 + 132.6 = 438.6 cm^2

Adding the areas of the base triangles and rectangular faces together, we get the total surface area of the triangular prism:
Total surface area = 141.94 + 438.6 = 580.54 cm^2

Therefore, the total surface area represented by this net of a triangular prism is approximately 580.54 cm^2.