The surface area of the composite solid is approximately 128.56 square feet.
Triangular prism:
Area of the base (triangle): 1/2 * base * height = 1/2 * 5 ft * 4 ft = 10 ft²
Area of each of the other faces (rectangles): height * width = 6 ft * 5 ft = 30 ft²
Since there are two of these rectangles, the total area of the rectangles is 2 * 30 ft² = 60 ft²
Adding the area of the base and the rectangles, the total surface area of the triangular prism is 10 ft² + 60 ft² = 70 ft²
Pyramid:
Area of each of the triangles: 1/2 * base * height
We need to find the heights of the triangles. We can use the Pythagorean theorem to do this.
In a right triangle where the hypotenuse is 6 ft and one leg is 5 ft, the other leg (the height of the triangle) is √(6² - 5²) = √11 ft.
Therefore, the area of each triangle is 1/2 * 5 ft * √11 ft ≈ 14.64 ft²
Since there are four triangles on the pyramid, the total area of the triangles is 4 * 14.64 ft² ≈ 58.56 ft²
Total surface area:
Adding the surface area of the triangular prism and the pyramid, the total surface area of the composite solid is 70 ft² + 58.56 ft² ≈ 128.56 ft²