a metalworker is creating decorative points in the form of a triangular pyramid to go on top of a fence she is building she wants to know the surface area of each pyramid ise surface area formula to find the surface area of each pyramid based on figure responses 9.5cm, 13.1cm, 18.2cm, 5.1cm
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.