How to calculate apothem?
Understand the Problem
The question is asking for the method to calculate the apothem of a polygon, which is the distance from the center of the polygon to the midpoint of one of its sides.
Answer
$\text{apothem} = \frac{s}{2 \tan(\pi / n)}$ or $\text{apothem} = R \cos(\pi / n)$
Answer for screen readers
The formula to calculate the apothem of a regular polygon can be either $\text{apothem} = \frac{s}{2 \tan(\pi / n)}$ or $\text{apothem} = R \cos(\pi / n)$
Steps to Solve
- Identify the given values and the type of polygon
The formula to calculate the apothem depends on the type of polygon (regular polygon). For a regular polygon, the apothem can be calculated using the side length or the number of sides (n) and the circumradius (R).
- Use the formula for the apothem with the side length
If you know the side length ( $$s$$) and the number of sides ( $$n$$) of the regular polygon, use the formula: $$ ext{apothem} = \frac{s}{2 \tan(\pi / n)}$$
- Use the formula for the apothem with the circumradius
If you know the circumradius ( $$R$$) and the number of sides ( $$n$$): $$ ext{apothem} = R \cos(\pi / n)$$
The formula to calculate the apothem of a regular polygon can be either $\text{apothem} = \frac{s}{2 \tan(\pi / n)}$ or $\text{apothem} = R \cos(\pi / n)$
More Information
The apothem is an important part of polygon geometry, especially in calculating the area of regular polygons.
Tips
A common mistake is confusing the length of the side (s) and the circumradius (R). Make sure you use the correct formula for the given values.
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