Regular Polygon Area
Cut into triangles (like a pizza). Find the area of one triangle.Multiply by the number of triangles.
The area of a regular polygon can be found using the formula:
A = 1/2 * apothem * perimeter
where A is the area of the polygon, apothem is the distance from the center of the polygon to its sides, and perimeter is the total length of all the sides of the polygon.
Another formula that can be used to find the area of a regular polygon is:
A = 1/2 * apothem * ns
where n is the number of sides in the polygon, and s is the length of each side.
To find the apothem of a regular polygon, you can use the formula:
apothem = (side length)/(2*tan(180/n))
where n is the number of sides in the polygon.
For example, let’s say we have a regular hexagon with a side length of 8 cm. We can find the apothem using:
apothem = (8)/(2*tan(180/6))
apothem = 6.928 cm
We can then find the perimeter of the hexagon using:
perimeter = 6 * 8
perimeter = 48 cm
Using the first formula, we can find the area of the hexagon:
A = 1/2 * 6.928 * 48
A = 166.56 cm^2
Alternatively, we can use the second formula to find the area of the hexagon:
A = 1/2 * 6.928 * 6 * 8
A = 166.56 cm^2
Therefore, the area of the regular hexagon is 166.56 cm^2.
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