A metalworker is creating decorative points in the form of a triangular pyramids to go on top of a fence she is building. She wants to know the surface area of each pyramid. use the surface area formulas to find the surface area of each pyramid based on the figure.
To find the surface area of a triangular pyramid, we need to calculate the area of all its faces.
A triangular pyramid has four faces - a base and three triangular faces.
The formula to find the surface area of a triangular pyramid is:
Surface Area = Area of Base + Area of Triangular Faces
1. Area of Base:
The base of a triangular pyramid is a triangle. To find its area, we need the length of the base and the height of the triangle. Let's call the base length B and the height H. The area of the base, A_base, is given by:
A_base = (1/2) * B * H
2. Area of Triangular Faces:
Each triangular face of the pyramid is also a triangle. The area of a triangle is given by the formula:
A_triangle = (1/2) * base * height
Let's call the base length of each triangular face T and the height of each face H. The surface area of the three triangular faces, A_faces, is given by:
A_faces = 3 * [(1/2) * T * H]
3. Total Surface Area:
Finally, we can calculate the total surface area of the triangular pyramid by summing the area of the base and the area of the triangular faces:
Surface Area = A_base + A_faces
= (1/2) * B * H + 3 * [(1/2) * T * H]
We can substitute the appropriate values for B, H, and T into this formula to find the specific surface area of each pyramid.