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
482 cm2
482 cm squared
384 cm2
384 cm squared
98 cm2
98 cm squared
128 cm2
To find the surface area of the triangular pyramid, we need to calculate the area of each face and then add them together.
Area of the base (equilateral triangle):
Area = (sqrt(3) / 4) x side^2
Area = (sqrt(3) / 4) x 15^2
Area = (1.732 / 4) x 225
Area = 0.433 x 225
Area = 97.87 cm^2
Area of one of the side faces (triangle):
Area = 1/2 x base x height
Area = 1/2 x 15 x 17
Area = 127.5 cm^2
Since the triangular pyramid has 3 identical side faces, the total surface area is:
3 x 127.5 (side faces) + 97.87 (base) = 382.37 cm^2
Therefore, the surface area of the triangular pyramid is approximately 383 cm^2.
Therefore, the closest answer choice is 384 cm2.