To find the surface area of a triangular pyramid, we need to account for four different triangles: the base triangle and three identical triangular faces.
The formula for the surface area of a triangular pyramid is:
Surface Area = Base Area + Lateral Area
The base area can be found using the formula for the area of a triangle:
Base Area = (1/2) * base * height
The lateral area can be found by summing the areas of the three identical triangular faces. Each triangular face has the same base and height.
Lateral Area = 3 * (1/2) * base * slant height
Therefore, the surface area of the triangular pyramid is:
Surface Area = (1/2) * base * height + 3 * (1/2) * base * slant height
A metal worker is creating decorative points in the form of triangular pyramids to go on top of the fence, she is building. She wants to know the surface area of each pyramid. Use the surface area formula to find the surface area of each pyramid based on the figure.
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