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 calculate the area of each triangular face and the base.
Let's denote the triangle formed by the base as triangle ABC. The surface area of a triangular pyramid can be calculated using the formula:
S = area(ABC) + area(ABD) + area(ACD) + area(BCD)
First, let's calculate the area of triangle ABC using its base and height. Let's denote the length of the base AB as b and the height AD as h.
Area(ABC) = (1/2) * base * height
= (1/2) * b * h
Next, let's calculate the area of each face of the pyramid. The triangle formed by each face has the same base as triangle ABC.
Area(ABD) = (1/2) * b * h
Area(ACD) = (1/2) * b * h
Area(BCD) = (1/2) * b * h
Now, we can calculate the surface area of the pyramid by summing up the areas of the triangular faces:
S = (1/2) * b * h + (1/2) * b * h + (1/2) * b * h + (1/2) * b * h
= 2 * (1/2) * b * h + 2 * (1/2) * b * h
= b * h + b * h
= 2 * b * h
Therefore, the surface area of each pyramid is 2 times the product of the base length and the height.