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. H= 3.5 cm, L= 3.9 cm, W= 4.5 cm.
To find the surface area of the triangular pyramid, we need to find the area of each face and then add them all together.
The formula for the surface area of a triangular pyramid is:
Surface Area = Base Area + (0.5 * Base Perimeter * Slant Height)
Let's find the area of the base first. The base is a triangle, so we can use the formula for the area of a triangle:
Base Area = (1/2) * base * height
Base Area = (1/2) * 3.9 cm * 4.5 cm
Base Area = 8.775 cm²
Next, we need to find the slant height. We can use the Pythagorean theorem to do this.
Slant Height = sqrt((height^2) + (0.5 * base)^2)
Slant Height = sqrt((3.5 cm)^2 + (0.5 * 3.9 cm)^2)
Slant Height = sqrt(12.25 cm² + 3.8025 cm²)
Slant Height = sqrt(16.0525 cm²)
Slant Height = 4.006 cm
Now we can calculate the surface area.
Surface Area = 8.775 cm² + (0.5 * 3.9 cm * 4.006 cm)
Surface Area = 8.775 cm² + (0.5 * 15.5614 cm²)
Surface Area = 8.775 cm² + 7.7807 cm²
Surface Area = 16.5557 cm²
Therefore, the surface area of each pyramid is approximately 16.5557 cm².