PLEASE answer correctly and Use the details i give you 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
A. 98 cm2
B. 482 cm2
C. 128 cm2
D. 384 cm2
B. 482 cm2
To calculate the surface area of the triangular pyramid, we first calculate the area of the base equilateral triangle:
Area of equilateral triangle = (sqrt(3) / 4) * side length^2
Area of base = (sqrt(3) / 4) * 15^2 = 97.43 cm2
Next, we calculate the area of one of the identical triangular faces using the formula for the area of a triangle:
Area of triangle face = (1/2) * base * height
Area of triangular face = (1/2) * 15 * 17 = 127.5 cm2
Since there are three identical triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 3 * 127.5 = 382.5 cm2
Therefore, the total surface area of the triangular pyramid is:
Total surface area = Area of base + Total area of triangular faces = 97.43 + 382.5 = 479.93 cm2
Rounded to the nearest whole number, the surface area is 482 cm2.