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.
(1 point)
3.5 cm
3.9cm
4.5cm
To find the surface area of a triangular pyramid, we need to find the area of the base and the area of the triangular faces.
Since the pyramid has a triangular base, we need to find the area of the base. To find the area of a triangle, we use the formula:
Area = (base * height) / 2
Given that the base of the pyramid is 3.5 cm and the height is 3.9 cm, we can calculate the area of the base as:
Base area = (3.5 cm * 3.9 cm) / 2 = 6.825 cm^2
Next, we need to find the area of the triangular faces. Since each face is an equilateral triangle, we can use the formula for the area of an equilateral triangle:
Area = (side length^2 * sqrt(3)) / 4
Given that the side length is 4.5 cm, we can calculate the area of each triangular face as:
Face area = (4.5 cm^2 * sqrt(3)) / 4 ≈ 5.301 cm^2
Finally, we can find the total surface area of the pyramid by summing the area of the base and the area of the triangular faces:
Total surface area = Base area + (3 * Face area)
= 6.825 cm^2 + (3 * 5.301 cm^2)
≈ 23.728 cm^2