A metalworker is creating decorative points in the form of 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 formula to find the surface area of each pyramid based on the figure.
To find the surface area of a triangular pyramid, we need to find the area of each triangular face and add them together.
The formula for the surface area of a triangular pyramid is:
S = 0.5 x base x height + 3 x area of base
Let's say the base of the pyramid is a triangle with base length 6 units and height 4 units. We can substitute these values into the formula to find the surface area:
S = 0.5 x 6 x height + 3 x area of base
First, let's find the area of the base triangle:
Area of base = 0.5 x base x height = 0.5 x 6 x 4 = 12 square units.
Now, let's find the surface area of the pyramid:
S = 0.5 x 6 x height + 3 x 12
S = 3 x height + 36 + 36
S = 3 x height + 72
So, the surface area of each triangular pyramid is 3 times the height plus 72 square units.