Find the surface area of pyramid that has a regular hexagonal base od edge 6 cm and a height of 8 cm.

Thank you so much

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To find the surface area of a pyramid, you need to calculate the area of each of its faces and then sum them up.

A pyramid with a regular hexagonal base will have six triangular faces and one hexagonal base. Let's calculate the surface area step by step:

1. Find the area of the hexagonal base:
The area of a regular hexagon is given by the formula A = (3√3 * s^2) / 2, where s is the length of each side.
In this case, the length of each side is 6 cm, so the area of the hexagonal base is:
A = (3√3 * 6^2) / 2 = (3√3 * 36) / 2 = (108√3) / 2 = 54√3 cm^2.

2. Find the area of each triangular face:
The formula for the area of a triangle is A = (1/2) * base * height, where base is one side of the triangle and height is the perpendicular distance from the base to the opposite vertex.
In this case, since the base is a regular hexagon, the base of each triangular face is 6 cm (the length of one side). The height of each triangular face is the same as the height of the pyramid, which is 8 cm.
Therefore, the area of each triangular face is:
A = (1/2) * 6 * 8 = 3 * 8 = 24 cm^2.

3. Calculate the total surface area:
Since there are six triangular faces and one hexagonal base, we need to multiply the area of each face by their respective counts.
Total surface area = (6 * 24) + 54√3
Total surface area = 144 + 54√3 cm^2

Therefore, the surface area of the given pyramid is 144 + 54√3 cm^2.