Understanding the Apothem: Calculation and Application in Geometry

Apothem

The term “apothem” is often used in geometry to refer to a line segment that connects the center of a regular polygon to one of its sides

The term “apothem” is often used in geometry to refer to a line segment that connects the center of a regular polygon to one of its sides. The apothem is perpendicular to the side it intersects, and it measures the shortest distance from the center of the polygon to its side.

To better understand the concept of an apothem, let’s consider a regular pentagon as an example. A regular pentagon is a polygon with five equal sides and five equal angles. The apothem of a regular pentagon is the line segment drawn from the center of the pentagon to one of its sides, forming a right angle with the side.

To calculate the length of the apothem for a regular polygon, you need to know the length of its side and the number of sides (n) it has. The formula to calculate the apothem length is:

Apothem = Side Length / (2 * tan(180° / n))

In this formula, tan represents the tangent function, and the angle in the denominator is in degrees.

Let’s use this formula to calculate the apothem length for a regular pentagon with a side length of 5 units. Substituting the values into the formula, we have:

Apothem = 5 / (2 * tan(180° / 5))

Now, let’s calculate the angle in degrees: 180° / 5 = 36°.

Next, we need to find the tangent of 36°:

tan(36°) ≈ 0.7265 (rounded to four decimal places)

Now, substitute this value into the formula:

Apothem = 5 / (2 * 0.7265)

Apothem ≈ 3.446 units (rounded to three decimal places)

Therefore, the apothem of the regular pentagon with a side length of 5 units is approximately 3.446 units.

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