We assume the question is asking for the total surface area of the triangular prism. That is the sum of the areas of the triangular bases and the lateral area consisting of three rectangles. As part of finding the lateral area, we must determine the length of the third side (hypotenuse) of the triangle.
The area of each of the triangles is half the product of base (6') and height (4'). Since there are two such triangles, their total area is the product of base and height, (6 ft)·(4 ft) = 24 ft².
The length of the hypotenuse (h) is given by the Pythagorean theorem as
... h = √((6 ft)² + (4 ft)²) = √(52 ft²) = 2√13 ft
Then the lateral area is the product of the height of the prism (8') and the perimeter of the triangular base, 4' + 6' + (2√13)'. That product is
... lateral area = (8 ft)((10 +2√13) ft) = (80 +16√13) ft²
The total area (T.A.) is the sum of base area and lateral area:
... T.A. = 24 ft² + (80 +16√13) ft² = (104 +16√13) ft²
