Use the image to answer the question.
An illustration shows a triangular pyramid made with rows of chocolate covered candies. The base measures 16 inches, the side of the triangular face measures 16 inches, and the vertical height is 13.86 inches.
Compute the surface area of the chocolate tower.
(1 point)
Responses
443.52 in.2
443.52 in. squared
554.4 in.2
554.4 in. squared
1,884.96 in.2
1,884.96 in. squared
460.64 in.2
The formula for the surface area of a triangular pyramid is:
Surface Area = base area + (0.5 * perimeter of base * slant height)
First, let's calculate the base area:
Base area = (1/2) * base * height
Base area = (1/2) * 16 * 13.86
Base area = 110.88 in^2
Next, let's calculate the slant height. We can use the Pythagorean theorem:
slant height = √(16^2 + (13.86/2)^2)
slant height = √(256 + 95.8794)
slant height = √351.8794
slant height ≈ 18.7569 inches
Now, let's calculate the perimeter of the base:
Perimeter of base = 3 * side
Perimeter of base = 3 * 16
Perimeter of base = 48 inches
Finally, we can plug all the values into the surface area formula:
Surface Area = 110.88 + (0.5 * 48 * 18.7569)
Surface Area = 110.88 + 450.42
Surface Area = 561.3 in^2
Therefore, the correct answer is not one of the options provided, as the calculated surface area is 561.3 in^2.