3.5 cm
3.9 cm
4.5 cm
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.
Help
To find the surface area of a triangular pyramid, you need to know the base area of the pyramid and the area of the triangular face.
The formula for the surface area of a triangular pyramid is:
Surface Area = Base Area + 0.5 * Perimeter of Base * Slant Height
First, let's find the base area of the pyramid. Since the base is a triangle, we can use the formula for the area of a triangle:
Base Area = (1/2) * base * height
Assuming the base of the pyramid is an equilateral triangle, we can calculate the base area with the given measurements.
For 3.5 cm:
Base Area = (1/2) * 3.5 cm * (3.5 cm * √3 / 2) = 3.81 cm^2 (approx.)
For 3.9 cm:
Base Area = (1/2) * 3.9 cm * (3.9 cm * √3 / 2) = 5.55 cm^2 (approx.)
For 4.5 cm:
Base Area = (1/2) * 4.5 cm * (4.5 cm * √3 / 2) = 7.29 cm^2 (approx.)
Next, we need to find the area of each triangular face of the pyramid. Again, since the base is an equilateral triangle, we can use the formula for the area of an equilateral triangle:
Face Area = (base * height) / 2
Since all sides of an equilateral triangle are equal, the base and height of the face are the same as the base and height of the base triangle. Therefore, the face area will be the same as the base area.
Finally, we can calculate the surface area of the pyramid using the formula mentioned earlier:
Surface Area = Base Area + 0.5 * Perimeter of Base * Slant Height
Since we don't have the slant height or the perimeter of the base, we cannot provide an exact surface area for each pyramid. More information is needed to calculate these values.