To find the surface area of a regular pyramid, we need to calculate the area of the base and the lateral faces.
The base of the pyramid is a regular triangle with side length 13 m. The area of an equilateral triangle is given by the formula:
Area_base = (√3/4) * side_length^2
Substituting the values, we have:
Area_base = (√3/4) * 13^2
Area_base ≈ 63.24 square meters (rounded to two decimal places)
The lateral faces of the pyramid are congruent isosceles triangles with base length 13 m and height 6.5 - √3 m. The area of an isosceles triangle is given by the formula:
Area_lateral = (1/2) * base_length * height
Substituting the values, we have:
Area_lateral = (1/2) * 13 * (6.5 - √3)
Area_lateral ≈ 49.16 square meters (rounded to two decimal places)
To find the total surface area, we add the area of the base and the area of the lateral faces:
Total_surface_area ≈ Area_base + (3 * Area_lateral)
Total_surface_area ≈ 63.24 + (3 * 49.16)
Total_surface_area ≈ 211.72 square meters (rounded to the nearest whole number)
Therefore, the surface area of the regular pyramid is approximately 212 square meters.