To find the surface area of a triangular pyramid, we need to calculate the area of the base and the lateral faces.
Given:
Base length of the triangular pyramid = 9.5 cm
Height of the triangular pyramid = 13.1 cm
Slant height of the triangular pyramid (lateral face height) = 18.2 cm
First, let's find the area of the base:
The base of a triangular pyramid is a triangle, and the area of a triangle can be calculated using the formula:
Area of triangle = (1/2) * base length * height
Area of base = (1/2) * 9.5 cm * 13.1 cm
Area of base = 61.975 cm²
Next, let's find the area of each of the lateral faces (the triangular sides):
The area of each lateral face can be calculated using the formula:
Area of triangle = (1/2) * base length * slant height
Area of each lateral face = (1/2) * 9.5 cm * 18.2 cm
Area of each lateral face = 86.81 cm²
Since we have four lateral faces, the total area of all the lateral faces is:
Total lateral face area = 4 * (Area of each lateral face)
Total lateral face area = 4 * 86.81 cm²
Total lateral face area = 347.24 cm²
Finally, to find the surface area of the triangular pyramid, we add the area of the base and the total area of the lateral faces:
Surface area = Area of base + Total lateral face area
Surface area = 61.975 cm² + 347.24 cm²
Surface area = 409.215 cm²
Therefore, the surface area of each triangular pyramid is approximately 409.215 cm².