Answer:
The surface area of the triangular prism is 138 square feet (ft²).
Explanation:
To calculate the surface area of a triangular prism, we need to find the area of each face and add them up. A triangular prism has two triangular faces and three rectangular faces.
Given:
Base of the triangle = 5 ft
Height of the triangle = 6 ft
Length of the rectangular face = 9 ft
Width of the rectangular face = 4 ft
Area of each triangular face = (1/2) x base x height
Area of each triangular face = (1/2) x 5 ft x 6 ft
Area of each triangular face = 15 ft²
Area of each rectangular face = length x width
Area of each rectangular face = 9 ft x 4 ft
Area of each rectangular face = 36 ft²
Now we can find the total surface area by adding up the areas of all the faces:
Total surface area = 2 x area of each triangular face + 3 x area of each rectangular face
Total surface area = 2 x 15 ft² + 3 x 36 ft²
Total surface area = 30 ft² + 108 ft²
Total surface area = 138 ft²
Therefore, the surface area of the triangular prism is 138 square feet (ft²).