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.
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
1 answer