Find the length of the apothem of a regular Pentagon with a side measuring 36 cm
Answers
24.75 cm is the length of the apothem of a regular Pentagon with a side measuring 36 cm.
In a regular pentagon, the apothem is the distance from the center of the pentagon to the midpoint of any side.
For a regular pentagon, all sides are equal in length and all interior angles are equal.
To find the apothem of a regular pentagon, you can use the following formula:
Apothem (a) = (Side Length) / (2 × tan(π / Number of sides))
In this case, for a regular pentagon, the number of sides (n) is 5, and the side length (s) is given as 36 cm.
Now, we can calculate the apothem:
Apothem (a) = 36 cm / (2×tan(π / 5))
First, let's calculate π / 5:
π / 5= 0.62832
Next, calculate the tangent of π / 5:
tan(π / 5) = 0.72654
Now, calculate the apothem:
Apothem (a) =36 cm / (2 × 0.72654)
= 36 cm / 1.45308
= 24.75 cm
So, the length of the apothem of the regular pentagon is approximately 24.75 cm.
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