Determine the total area of the THREE lateral faces of this triangular prism.
A. 48 square inches
B. 96 square inches
C. 188 square inches
D. 448 square inches
i want a right answer
To determine the total area of the three lateral faces of a triangular prism, we need to find the area of each lateral face and then add them together.
The formula to calculate the lateral area of a triangular prism is the perimeter of the base (triangle) multiplied by the height of the prism.
Given that the base of the triangular prism is a triangle and the perimeter of the base is 24 inches (6 + 8 + 10), and the height of the prism is 8 inches, we can calculate the area of each lateral face.
Area of the lateral face 1 = 24 in * 8 in = 192 square inches
Area of the lateral face 2 = 24 in * 8 in = 192 square inches
Area of the lateral face 3 = 24 in * 8 in = 192 square inches
Adding the areas of all three lateral faces:
192 + 192 + 192 = 576 square inches
Therefore, the correct answer is not among the options provided, but the total area of the three lateral faces of the triangular prism is 576 square inches.
thats not a answer A. 48 B. 96 C.188 D.448
Apologies for the misunderstanding. Let's calculate the total area of the three lateral faces of the triangular prism using the given options.
The perimeter of the triangular base is 6 + 8 + 10 = 24 inches.
The height of the prism is 8 inches.
Area of each lateral face = Perimeter of base * height = 24 * 8 = 192 square inches
Since we have three lateral faces, the total area of the three lateral faces is:
3 * 192 = 576 square inches
Since 576 square inches is not among the given options, let's compare the closest option to the correct total area:
The closest option to 576 square inches is 448 square inches (option D), but the correct total area of the three lateral faces of the triangular prism is 576 square inches.