To find the surface area of the regular pyramid, you need to find the area of the hexagonal base and the area of the six triangles that make up the sides of the pyramid.
1. Area of the hexagonal base:
Area = 6 * (1/2) * base side length * apothem
Area = 6 * (1/2) * 10 * (5√3)
Area = 6 * 5 * 10 * √3
Area = 300√3
2. Area of the six triangles:
Area = 6 * (1/2) * base side length * slant height
Area = 6 * (1/2) * 10 * 13
Area = 6 * 5 * 13
Area = 390
Total surface area = Area of base + Area of sides
Total surface area = 300√3 + 390
Total surface area ≈ 650 m2
Therefore, the surface area of the regular pyramid is approximately 650 m2. The closest option is 650 m2.
For the following question, find the surface area of the regular pyramid shown to the nearest whole number.
A hexagonal pyramid is shown. A red segment extends from the center of the hexagonal base to a side. A small square is located at the intersection of this segment with the side. The measure of the segment is 5 start root 3 end root. The length of a side of the hexagonal base is 10 meters. The slant height is 13 meters.
(1 point)
Responses
1,300 m2
1,300 m 2
390 m2
390 m 2
650 m2
650 m 2
628 m2
1 answer