Calculate the lateral surface of a pyramid
The formulas for calculating the sizes of geometric figures, such as the outer surface of a pyramid, change with the design of the figures. Basic formulas help you to keep track of things.
What you need:
- Formulas for different pyramids
In the case of the outer surface of a pyramid, you must first differentiate the type of pyramid in order to choose the appropriate formula for calculation. Pyramids can be square, three-sided, or six-sided. As a rule, one assumes regular pyramids, i.e. symmetrical aspect ratios. Note that a circular cone is not a pyramid.
Formulas for the outer surface
- When calculating the surface area of a pyramid, the base sides are always designated with the letter a and the height with h. The height h always represents the shortest length from the base to the top of the pyramid and not the length of the outside of a pyramid.
- To calculate the surface area of a square pyramid, you need the following formula: M = 2ah.
- When calculating a three-sided pyramid, a different formula applies, namely: M = 3 / 2ah. For a six-sided pyramid, use the formula: M = 3ah.
- At least two variables must be given in order to calculate the missing size by rearranging the formula. If there are no figures, you can only solve the outer surface depending on the unknown variables a, h or M.
Calculate the base area - this is how it works with the pyramid
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Calculate truncated pyramids correctly
- Other formulas apply to truncated pyramids. A pyramid without a tip is called a stump.
- Note that a square pyramid as a truncated triangle requires the following formula for calculating the surface area: M = 2 (a1+ a2)H. A.1 denotes the basic side length a2 the base side length of the stump.
- The following applies to three-sided truncated pyramids: M = 3/2 (a1 + a2)H.
- For the six-sided pyramid, use the formula to calculate the surface area: M = 3 (a1 + a2)H.
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