Contents
In this publication, we will look at how you can calculate the surface area of various types of regular pyramids: triangular, quadrangular and hexagonal.
Regular pyramid – This is a pyramid, the top of which is projected into the center of the base, which is a regular polygon.
Formula for the area of a regular pyramid
1. General formula
The area (S) of the full surface of the pyramid is equal to the sum of the area of its lateral surface and the base.
Sfull = Sside. + Smain
The side face of a regular pyramid is an isosceles triangle.
The area of a triangle is calculated by the formulas:
1. Through the length of the base (a) and height (h):
2. Through the base (a) and side (b):
The formula for the area of uXNUMXbuXNUMXbthe base of a regular pyramid depends on the type of polyhedron. Next, we will look at the most popular options.
2. Area of a regular triangular pyramid
Base: equilateral triangle.
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| Area | Formula |
| base | |
| side surface | |
| full |
L (apopheme) – a perpendicular line drawn from the top of the pyramid to the edge of the base. Those. the apothem of the pyramid is the height (h) of its lateral face.
3. Area of a regular quadrangular pyramid
Base: square.
| Area | Formula | |
| base | side surface |  «> |
| full |  «> |
4. Area of a regular hexagonal pyramid
Base: regular hexagon
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| Formula | |
| base | |
| side surface |  «> |
| full |