Question

3.5 cm

3.9 cm

SE TOOLS

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4.5 cm

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OUTLINE

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)

Answer 1

To calculate the surface area of a triangular pyramid (or tetrahedron), you can use the following formula:

\[
\text{Surface Area} = \text{Base Area} + \text{Lateral Area}
\]

For a triangular pyramid, the base is a triangle, and the lateral area can be calculated based on the triangular faces.

1. **Base Area**:
If the base of the pyramid is a triangle, you can calculate its area using the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Alternatively, if you have the lengths of the sides of the triangle, you can also use Heron's formula:
\[
s = \frac{a + b + c}{2} \\
\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}
\]
Where \(a, b,\) and \(c\) are the sides of the triangle, and \(s\) is the semi-perimeter.

2. **Lateral Area**:
The lateral area consists of the areas of the three triangular sides. If you know the height from the apex of the pyramid to the base and the lengths of the edges coming from the apex to each vertex of the base, you can calculate the area of each triangular face similarly. For each triangular face:
\[
\text{Area of triangular face} = \frac{1}{2} \times \text{base} \times \text{height}
\]

3. **Adding the Areas**:
Finally, add up the area of the base and the areas of the three triangular faces to get the total surface area.

If you provide the specific dimensions for the base and the height of the triangular pyramid, I can help you calculate the surface area.