# Circle Basics

A circle is a round, circular, polygon.

The many parts of a circle are shown above, such as the radius, sector, and segment. We will be going over each of these parts in great detail.

Let’s try some examples using these equations.

What is the area of the sector of the circle on the right?

The formula of the area of a sector is angle/360 degrees * pi * radius ^ 2. Plug in the values to get the answer.

angle/360 degrees * pi * radius ^ 2 = 315 degrees / 360 degrees * pi * 11 ft ^ 2 = 105.875*pi ft ^ 2 (you do not have to multiply pi out)

What is the area of the segment of the circle below?

The equation for the area of a segment of a circle is (radius ^ 2) / 2 * ((pi / 180) * angle - sin(angle)). We are given the angle and the numbers so we plug the numbers in. To calculate the sin of the angle, you can use a calculator.

(radius ^ 2) / 2 * ((pi / 180) * angle - sin(angle)) = 12 ^ 2 / 2 * ((pi / 180) * 120 - sin(120)) = 88.44 units ^ 2

What is the arc of the circle below? The radius is 5.

The equation to find the area of an arc of a circle is angle / 360 * circumference. Now, we just plug in our values to get the answer!

angle / 360 * circumference = 123 / 360 * 2 * 5 * pi = 10.733 units ^ 2

Now let’s try a quiz!

Sources:

https://www.aplustopper.com/parts-of-the-circle/

https://www.omnicalculator.com/math/circle

https://www.mathopenref.com/segment.html

https://www.onlinemath4all.com/arcs-and-chords.html

https://www.piday.org/calculators/circumference-calculator/

http://nwatson1.weebly.com/uploads/1/0/7/1/10717301/2-hw_area_of_a_segment_of_a_sector.pdf