Solution
- The base is a regular hexagon. This implies that it can be divided into equal triangles.
- These equal triangles can be depicted below:
- If each triangle subtends an angle α at the center of the hexagon, it means that we can find the value of α since all the α angles are subtended at the center of the hexagon using the sum of angles at a point which is 360 degrees.
- That is,
- We also know that regular hexagon is made up of 6 equilateral triangles.
- Thus, the formula for finding the area of an equilateral triangle is:
- Thus, the area of the hexagon is:
- With the above formula we can find the length of the regular hexagon as follows:
- The formula for the volume of a hexagonal pyramid is:
- Thus, the volume of the pyramid is