Area of Regular Polygon
A = 1/2(a)(p)
The formula to calculate the area of a regular polygon is:
A = (1/2) * n * a * s
Where A is the area of the polygon, n is the number of sides of the polygon, a is the length of each side of the polygon, and s is the length of apothem (the perpendicular distance from the center of the polygon to a side).
To use this formula, you need to know the value of n, a, and s. If you’re given the perimeter (P) of the polygon instead of the length of each side, you can calculate a as:
a = P / n
And if you’re given the radius (r) of the polygon instead of the apothem, you can calculate s as:
s = r * cos(π/n)
Once you have all the values, you can plug them into the formula and solve for the area of the polygon.
For example, let’s say you’re given a regular hexagon with a side length of 5 cm. To find the area, you would first need to find s. The radius of the hexagon can be found by dividing the apothem by cos(π/6) (which is equivalent to √3/2), so:
r = s / cos(π/6) = s * 2/√3
Since the side length is also given, we can use the formula for the perimeter to find the value of a:
P = 6a = 30 cm => a = 5 cm
Now, substituting the values of n, a, and s in the area formula, we get:
A = (1/2) * 6 * 5 cm * (5/2) cm * √3 = 64.95 cm^2
Therefore, the area of the regular hexagon is about 64.95 cm^2.
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