A metal feeding trough is in the shape of a triangular prism with one of the faces missing. The base of the trough is an equilateral triangle with sides of length 3.5 feet and a height of 4 feet. If the trough is 15 feet long, how much metal was used to construct the trough?
66.5 ft
119 ft
171.5 ft
194 ft
pls! I need an answer soon >n<
I’m sorry I do not have a complete answer- i just turned my answer to the question in and it was wrong so all I have for you is that it is not C/171.5ft^2, sorry it isn’t much help.
To find the amount of metal used to construct the trough, we need to calculate the surface area of the trough.
The trough has two triangular bases and three rectangular faces.
To find the surface area of the triangular bases, we can use the formula: Area = (1/2) * base * height
The base of the triangular base is an equilateral triangle with sides of length 3.5 feet.
The height of the triangular base is 4 feet.
Plugging these values into the formula gives us:
Area of one triangular base = (1/2) * 3.5 * 4 = 7 square feet
Since there are two triangular bases, the total area for the triangular bases is:
Total area of triangular bases = 2 * 7 = 14 square feet
To find the surface area of the rectangular faces, we can use the formula: Area = length * width
The length of the rectangular faces is 15 feet.
The width of the rectangular faces is the same as the height of the triangular base, which is 4 feet.
Plugging these values into the formula gives us:
Area of one rectangular face = 15 * 4 = 60 square feet
Since there are three rectangular faces, the total area for the rectangular faces is:
Total area of rectangular faces = 3 * 60 = 180 square feet
Now, we can find the total surface area of the trough by adding the areas of the triangular bases and the rectangular faces together:
Total surface area = Total area of triangular bases + Total area of rectangular faces
= 14 + 180
= 194 square feet
Therefore, 194 feet of metal was used to construct the trough.
To determine how much metal was used to construct the trough, we need to find the surface area of the trough.
First, let's calculate the area of the base of the trough, which is an equilateral triangle. The formula for the area of an equilateral triangle is (sqrt(3)/4) * s^2, where s is the length of a side. In this case, s = 3.5 feet, so the area of the base is:
Area_base = (sqrt(3)/4) * (3.5)^2 = 9.555 ft^2 (rounded to three decimal places)
Next, we need to find the area of the two lateral faces of the trough. Since the trough is a triangular prism, the area of the lateral faces is equal to the perimeter of the base multiplied by the height of the trough. The perimeter of an equilateral triangle is equal to 3 times the length of a side. Therefore, the perimeter of the base is:
Perimeter_base = 3 * 3.5 = 10.5 ft
Now, we can find the area of the two lateral faces:
Area_lateral = Perimeter_base * height = 10.5 * 4 = 42 ft^2
Finally, to calculate the total surface area of the trough, we add the areas of the base and the two lateral faces:
Total_surface_area = Area_base + 2 * Area_lateral = 9.555 + 2 * 42 = 93.555 ft^2 (rounded to three decimal places)
Therefore, approximately 93.555 feet of metal was used to construct the trough. None of the given answer choices match this result, so it seems there is an error in the problem or the answer choices provided.