Apothem facts for kids
The apothem (say 'APP-uh-them') is a special line inside a regular polygon. It goes from the very center of the polygon straight to the middle of one of its sides. This line always forms a perfect right angle (90 degrees) with the side. The word 'apothem' can also mean the length of this line. You'll only find apothems in regular polygons, which are shapes with all sides and angles equal. In any one regular polygon, all its apothems are exactly the same length!
How Apothems Help Find Area
The apothem is super useful for finding the area of any regular polygon. Imagine you have a regular polygon, like a hexagon or an octagon. If you know the length of its apothem (let's call it a) and the length of one of its sides (let's call it s), you can find its area!
Here's the formula: Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): A = {nsa \over 2} Let's break down what each letter means:
- A stands for the Area of the polygon.
- n is the number of sides the polygon has. (For example, a hexagon has 6 sides, so n=6).
- s is the length of one side of the polygon.
- a is the apothem length.
You can also think of it this way: the total distance around the polygon is its perimeter. The perimeter (let's call it p) is simply the number of sides (n) multiplied by the length of one side (s), so p = ns.
Using the perimeter, the formula becomes even simpler: Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): A = {pa \over 2} This means the area is half of the perimeter multiplied by the apothem. It's a quick way to find the area of any regular polygon!
See also
In Spanish: Apotema para niños
