Final answer:
To find the surface area of the pyramid, calculate the combined area of the triangles and add it to the area of the base. However, the given options do not match the calculated surface area of 151.9 m^2, indicating a possible error.
Step-by-step explanation:
To find the surface area of the regular pyramid with a net consisting of a pentagon and five equilateral triangles, the following steps should be taken:
- Calculate the area of the pentagonal base, which is given as 61.9 square meters.
- Find the area of one of the equilateral triangles.
- Multiply the area of one triangle by 5 since there are 5 identical triangles.
- Add the area of the pentagonal base to the combined area of the triangles to find the total surface area.
The formula for the area of a triangle is 1/2 × base × height. Using the given measurements for one of the equilateral triangles, the base is 6 meters (which matches the side of the pentagon), and the height is 6 meters. So, the area of one triangle would be:
Area of one triangle = 1/2 × base × height = 1/2 × 6 m × 6 m = 18 m²
Then the combined area of the five triangles is:
Combined area of triangles = 5 × 18 m² = 90 m²
Finally, adding this to the area of the base gives us:
Total surface area = Area of base + Combined area of triangles = 61.9 m² + 90 m² = 151.9 m²
The options provided do not include 151.9 m², so it appears that there may be an error in the provided options, or in the understanding of the question as posed.