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Area Hex

The document explains the concept of an apothem, which is a line from the center of a polygon to one of its sides. It provides methods to calculate the apothem and the area of a 1000-sided inscribed polygon within a circle of radius 10, using trigonometric functions and the Pythagorean theorem. The area of the polygon is calculated to be approximately 314.16, which is consistent with the area of the circle.

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Andy Ortiz
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33 views3 pages

Area Hex

The document explains the concept of an apothem, which is a line from the center of a polygon to one of its sides. It provides methods to calculate the apothem and the area of a 1000-sided inscribed polygon within a circle of radius 10, using trigonometric functions and the Pythagorean theorem. The area of the polygon is calculated to be approximately 314.16, which is consistent with the area of the circle.

Uploaded by

Andy Ortiz
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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What is the apothem?

A line going from the center of


The polygon to on of the sides.

Since O==10,
Since O 10,X = 20.
X = 20.
P = 6*20 = 120
P
A== 6*X = 6*20 = 120

Method 1: Use the angle Method 2: Use Pythagorean theorem


1. Use one value that 1 have a^2+b^2=c^2
2. Find value I don’t have
(c is always the hypotenuse, a and b
What do we want? don’t matter:ONLY for Pythagorean
We want O. theorem)
We have : angle and H

sin(ϴ) = O/H
sin(30) = O/20
O = 20sin(30)
O = 10
Let C be a circle of radius 10. We will inscribe a polygon inside the
circle. Let P be the inscribed polygon with 1000 sides.
The apothem of the 1000-gon be 10. Find the area of the 1000-gon.
1) What is the angle theta?
360/1000/2 = .18

sin(.18) = O/10
O=10sin(.18)
= .0314
X = 2*O
= .0628
P = .0628*1000 = 62.83
A = aP/2
= (10)(62.83)/2
314.15878

A = piR^2
= (3.1415926)*(10)^2
= 314.15926

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