3.5cm
3.9cm
4.5cm
a metalworker is creating decorative points in the form of a triangular pyramid 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.
___ cm^2
To find the surface area of each pyramid, we need to calculate the area of each of its faces and add them together.
Given that the base of the pyramid is a triangle, we can use the formula for the area of a triangle, which is 1/2 * base * height.
Since it is a triangular pyramid, we have 3 identical triangles as faces.
Let's calculate the surface area for the first pyramid with dimensions:
Base: 3.5 cm
Height: 3.5 cm
Area of one triangular face: (1/2) * 3.5 cm * 3.5 cm = 6.125 cm^2
Since there are 3 identical triangular faces, the total surface area for this pyramid would be:
Total surface area = 3 * 6.125 cm^2 = 18.375 cm^2
Let's calculate the surface area for the second pyramid with dimensions:
Base: 3.9 cm
Height: 3.9 cm
Area of one triangular face: (1/2) * 3.9 cm * 3.9 cm = 7.605 cm^2
Since there are 3 identical triangular faces, the total surface area for this pyramid would be:
Total surface area = 3 * 7.605 cm^2 = 22.815 cm^2
Finally, let's calculate the surface area for the third pyramid with dimensions:
Base: 4.5 cm
Height: 4.5 cm
Area of one triangular face: (1/2) * 4.5 cm * 4.5 cm = 10.125 cm^2
Since there are 3 identical triangular faces, the total surface area for this pyramid would be:
Total surface area = 3 * 10.125 cm^2 = 30.375 cm^2
So, the surface areas of the pyramids with dimensions 3.5 cm, 3.9 cm, and 4.5 cm are 18.375 cm^2, 22.815 cm^2, and 30.375 cm^2 respectively.