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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

98 cm2
98 cm squared

128 cm2
128 cm squared

384 cm2
384 cm squared

482 cm2

Answer 1

To find the surface area of the triangular pyramid, we need to calculate the area of each of the four triangular faces and add them together.

The area of the base equilateral triangle can be calculated using the formula:

Area = (base * height) / 2
Area = (15 * 13) / 2 = 97.5 cm2

Since there are three identical faces with the same dimensions, we can calculate the area of a single triangular face using the formula:

Area = (1/2) * base * slant height
Area = (1/2) * 15 * 17 = 127.5 cm2

Now we add up the areas of the four triangular faces to find the total surface area:

97.5 (base) + 127.5 (three faces) = 382.5 cm2

Therefore, the surface area of the triangular pyramid is 382.5 cm2. So the closest option is 384 cm2.