what is the surface area of a triangle the height is 5.1 the prism length is 30.5 the slant height of the triangle base is 28.4 the base of the triangular prism is 27.9
The surface area of a triangular prism can be calculated by adding the area of the two triangular bases and the three rectangular sides.
First, we need to calculate the area of one of the triangular bases:
Area of triangle = (1/2) * base * height
Area of triangle = (1/2) * 27.9 * 5.1
Area of triangle = 71.145
Next, we need to calculate the area of the rectangular sides. The three sides are essentially rectangles with a base equal to the perimeter of the triangular base and a height equal to the prism length.
Perimeter of triangle base = 3 * 27.9
Perimeter of triangle base = 83.7
Area of rectangle side = base * height
Area of rectangle side = 83.7 * 30.5
Area of rectangle side = 2551.85
Finally, we can calculate the total surface area of the triangular prism by adding the two triangular bases and three rectangular sides:
Surface area = 2 * Area of triangle + 3 * Area of rectangle side
Surface area = 2 * 71.145 + 3 * 2551.85
Surface area = 142.29 + 7655.55
Surface area = 7797.84
Therefore, the surface area of the triangular prism is 7797.84 square units.