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. The slant height is 3.5 cm, the base is 3.9 cm, and the edge length is 4.5 cm.
(1 point)
The formula to find the surface area of a triangular pyramid is:
Surface Area = base area + lateral area
First, let's find the base area. The base is a triangle, so we can use the formula for the area of a triangle:
Base Area = (1/2) * base * height
In this case, the base is 3.9 cm and the height is the slant height, which is 3.5 cm. Plugging in these values into the formula, we get:
Base Area = (1/2) * 3.9 cm * 3.5 cm
= 6.825 cm^2
Next, let's find the lateral area. The lateral area consists of four congruent triangles, so we can use the formula for the area of a triangle:
Lateral Area = 4 * (1/2) * base * slant height
In this case, the base is 3.9 cm and the slant height is 3.5 cm. Plugging in these values into the formula, we get:
Lateral Area = 4 * (1/2) * 3.9 cm * 3.5 cm
= 27.3 cm^2
Finally, we can find the surface area by adding the base area and the lateral area:
Surface Area = base area + lateral area
= 6.825 cm^2 + 27.3 cm^2
= 34.125 cm^2
Therefore, the surface area of each pyramid is 34.125 square centimeters.