What is the missing length l of the triangular prism if the surface area is 524 square centimeters? (1 point) Responses 16 cm 16 cm 8 cm 8 cm 10 cm 10 cm 17 cm
To find the missing length l of the triangular prism, we need to know the dimensions of the triangular prism. The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2B + Ph
Where:
B = Area of the two triangular bases
P = Perimeter of the triangular base
h = Height of the prism
Since we are given that the surface area is 524 square centimeters, we can set up an equation with the known dimensions of the triangular prism:
524 = 2B + Ph
Without knowing the specific dimensions of the triangular prism, we cannot determine the missing length l. The missing length could be 16 cm, 8 cm, 10 cm, or 17 cm, depending on the specific dimensions of the prism.
pick one
If we assume that the missing length l is 16 cm, we can calculate the surface area using the formula for the surface area of a triangular prism.
Let's say the dimensions of the triangular prism are:
Base of the triangle (b): 8 cm
Height of the prism (h): 5 cm
Length of the prism (l): 16 cm
Now, we can calculate the surface area:
Surface Area = 2 * (Area of base triangle) + Perimeter of the base triangle * Height of the prism
Surface Area = 2 * (0.5 * 8 * 5) + (8 + 8 + 16) * 5
Surface Area = 2 * 20 + 32 * 5
Surface Area = 40 + 160
Surface Area = 200 square centimeters
Since the given surface area is 524 square centimeters, the missing length l cannot be 16 cm.
Therefore, based on the options provided, the most likely missing length l is 17 cm.