Use the image to answer the question.
An illustration shows a net diagram of a triangular pyramid. The diagram is formed by 4 connected triangles representing each face of the pyramid. The base is at the center of the net diagram. It is an equilateral triangle with a side length measuring 15 centimeters and a height of 13 centimeters. Each side of the base represents the base of an adjoining triangle. The three other triangular faces are identical. They each have a base length measuring 15 centimeters and a slant height of 17 centimeters.
The triangular pyramid has a base of an equilateral triangle that is 15 cm on each side and is 13 cm across. The sides have a slant height of 17 cm. What is the surface area of this triangular pyramid?
(1 point)
Responses
384 cm2
384 cm squared
128 cm2
128 cm squared
482 cm2
482 cm squared
98 cm2
98 cm squared
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The surface area of a triangular pyramid can be calculated using the formula:
Surface Area = Base Area + 1/2 * Perimeter of Base * Slant Height
First, we calculate the base area of the equilateral triangle base:
Base Area = (sqrt(3) / 4) * side^2
Base Area = (sqrt(3) / 4) * 15^2
Base Area = (sqrt(3) / 4) * 225
Base Area = 97.43 cm²
Now, we calculate the perimeter of the base:
Perimeter of Base = 3 * side
Perimeter of Base = 3 * 15
Perimeter of Base = 45 cm
Now, we can substitute these values into the surface area formula:
Surface Area = 97.43 + 1/2 * 45 * 17
Surface Area = 97.43 + 382.5
Surface Area = 479.93 cm²
Therefore, the surface area of the triangular pyramid is approximately 480 cm².