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?
482 cm2 482 cm squared 384 cm2 384 cm squared 98 cm2 98 cm squared 128 cm2
The surface area of a triangular pyramid can be calculated using the formula:
Surface Area = base area + 1/2 * perimeter of base * slant height
First, let's calculate the base area of the equilateral triangle:
Base area = (sqrt(3)/4) * side^2
Base area = (sqrt(3)/4) * 15^2
Base area = (sqrt(3)/4) * 225
Base area = (1.732/4) * 225
Base area = 43.30125 cm^2
Next, let's calculate the perimeter of the base:
Perimeter = 3 * side
Perimeter = 3 * 15
Perimeter = 45 cm
Now, let's substitute the base area, perimeter, and slant height into the formula:
Surface Area = 43.30125 + 1/2 * 45 * 17
Surface Area = 43.30125 + 1/2 * 765
Surface Area = 43.30125 + 382.5
Surface Area = 425.80125 cm^2
Therefore, the surface area of the triangular pyramid is approximately 425.8 cm^2.
that answers are
482 cm2 482 cm squared 384 cm2 384 cm squared 98 cm2 98 cm squared 128 cm2
I apologize for the error in my previous response.
Let's correct the calculation:
Base area of the equilateral triangle = (sqrt(3) / 4) * (side length)^2
Base area = (sqrt(3) / 4) * 15^2
Base area = (1.732 / 4) * 225
Base area = 43.3 cm²
Perimeter of the base = 3 * side length
Perimeter of the base = 3 * 15
Perimeter of the base = 45 cm
Surface Area = Base area + 1/2 * Perimeter of base * slant height
Surface Area = 43.3 + 1/2 * 45 * 17
Surface Area = 43.3 + 382.5
Surface Area = 425.8 cm²
Therefore, the surface area of the triangular pyramid is approximately 425.8 cm².
Given the options, the closest answer is 482 cm².