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 length is 3.9, the width is 4.5, and the height is 3.5
To find the surface area of a triangular pyramid, we need to calculate the area of each triangular face and the area of the base.
The triangular faces are isosceles triangles, so we can calculate their area using the formula A = (1/2) * base * height.
Let's calculate the area of one triangular face:
base = 3.9
height = 3.5
A = (1/2) * 3.9 * 3.5
A = 6.825 square units
Since there are four triangular faces in a pyramid, the total area of the triangular faces is:
4 * 6.825 = 27.3 square units
The base of the pyramid is a rectangular shape, so we can calculate its area using the formula A = length * width.
Let's calculate the area of the base:
length = 3.9
width = 4.5
A = 3.9 * 4.5
A = 17.55 square units
Now, we can find the total surface area of the pyramid by adding the areas of the triangular faces and the base together:
27.3 + 17.55 = 44.85 square units
Therefore, the surface area of each triangular pyramid is 44.85 square units.