To find the surface area of a triangular pyramid (also known as a tetrahedron), we need to calculate the area of the base and the areas of the triangular lateral faces.
1. Calculate the area of the base:
The base of the pyramid is a triangle. The formula for the area \( A \) of a triangle is given by:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base is 5 inches, and the height of the base triangle is 4.3 inches:
\[ A = \frac{1}{2} \times 5 \times 4.3 = \frac{1}{2} \times 21.5 = 10.75 \text{ in}^2 \]
2. Calculate the area of the three triangular lateral faces:
Each lateral triangular face has a base of 5 inches and a slant height of 6 inches. The area of each triangular face is calculated similarly:
\[ \text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 6 = \frac{1}{2} \times 30 = 15 \text{ in}^2 \]
Since there are three triangular faces, the total area for all three sides is:
\[ \text{Total area of lateral faces} = 3 \times 15 = 45 \text{ in}^2 \]
3. Total surface area of the pyramid:
Now, we add the area of the base to the total area of the lateral faces:
\[ \text{Total Surface Area} = \text{Area of base} + \text{Area of lateral faces} \] \[ = 10.75 + 45 = 55.75 \text{ in}^2 \]
Thus, the surface area of the chocolate pyramid is 55.75 in.².
So the correct response is:
55.75 in.2 55.75 in. squared
1 answer