The surface area of the triangular prism shown as a net can be calculated by finding the areas of each face of the prism and adding them together.
First, we calculate the area of the rectangle which is the base of the prism:
Area = length x width
Area = 3m x 8m
Area = 24m^2
Next, we calculate the area of the two triangles which are the sides of the prism. The two missing values indicate that these triangles are both isosceles triangles.
To find the height of the triangle (the segment perpendicular to the base from the tip of the triangle), we can use the Pythagorean theorem:
a^2 + b^2 = c^2
2.6^2 + h^2 = 13^2
6.76 + h^2 = 169
h^2 = 162.24
h ≈ 12.74m
Now, we can calculate the area of one of the triangles:
Area = 1/2 x base x height
Area = 1/2 x 3m x 12.74m
Area ≈ 19.11m^2
The total surface area of the triangular prism is:
24m^2 + 2(19.11m^2) = 62.22m^2
So, the surface area of the triangular prism shown as a net is approximately 62.2m^2.