USE THE NET TO FIND THE SURFESE AREA OF THE TRIANGULAR PRIZIM WITH EQUALATERAL BASE
A 84 IN.2
B 357 IN.2
C 273 IN.2
D 175 IN.2
To find the surface area of a triangular prism with an equilateral base, we need to calculate the area of the two triangular bases and the three rectangular sides.
The formula for the surface area of a triangular prism is:
Surface Area = 2*(area of triangular base) + (perimeter of base)*(height)
Since the base is an equilateral triangle, we can calculate the area of the base using the formula:
Area = (side length)^2 * sqrt(3) / 4
Given that the base area is 84 in^2, we can solve for the side length of the equilateral triangle:
84 = (side length)^2 * sqrt(3) / 4
side length = sqrt((84 * 4) / sqrt(3)) = sqrt(336) = 4sqrt(21) in
Now, we can calculate the perimeter of the base:
Perimeter = 3 * side length = 3 * 4sqrt(21) = 12sqrt(21) in
Next, we calculate the height of the triangular prism. Let's assume the height to be h in.
Now, we can use the formula for the surface area of the triangular prism to calculate the surface area in terms of h:
Surface Area = 2*(84) + (12sqrt(21))*h
We do not have enough information to calculate the surface area in numerical values, so the correct answer cannot be determined without knowing the height of the triangle prism.