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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

482 cm2
482 cm squared

128 cm2
128 cm squared

384 cm2

Answer 1

The surface area of a triangular pyramid can be calculated by finding the area of the base and adding the areas of the three triangular faces.

The area of the equilateral base triangle can be found using the formula A = (√3 / 4) * s^2, where s is the side length of the equilateral triangle.

A = (√3 / 4) * 15^2
A = (√3 / 4) * 225
A = (√3 / 4) * 225
A = 97.43 cm^2

The area of each of the three identical triangular faces can be found using the formula A = (1/2) * b * h, where b is the base length and h is the slant height.

Each face has an area of (1/2) * 15 * 17 = 127.5 cm^2

The total surface area is then the sum of the base area and three face areas:

97.43 + (3 * 127.5) = 97.43 + 382.5 = 479.93

Therefore, the surface area of the triangular pyramid is approximately 480 cm^2.

The closest answer choice is 482 cm^2, so the correct response is:

482 cm squared