### Video Transcript

The area of a circle is 227 square
centimeters and the central angle of a segment is 120 degrees. Find the area of the segment,
giving the answer to two decimal places.

Weβre told in the question that the
central angle of a segment is 120 degrees. And we need to calculate the area
of this segment. When the angle of a segment is
given in degrees, we can calculate the angle of this segment by subtracting the area
of the triangle from the area of the sector. The area of the sector is equal to
π over 360 multiplied by ππ squared. The area of the triangle is equal
to a half π squared multiplied by sin π. We are told in the question that
the area of the circle is equal to 227 square centimeters. This means that ππ squared equals
227. Dividing both sides of this
equation by π gives us π squared is equal to 227 over π.

We can now substitute these into
both of our formulas. The area of the sector is equal to
120 over 360 multiplied by 227. This can be simplified to one-third
multiplied by 227 or 227 over three. The area of the triangle can be
calculated by multiplying a half by 227 over π by sin of 120 degrees. Sin of 120 degrees is equal to root
three over two. The area of the segment can
therefore be calculated by subtracting a half multiplied by 227 over π multiplied
by root three over two from 227 over three. Typing this into the calculator
gives us 44.37875 and so on. As we need to round our answer to
two decimal places, the key or deciding number is the eight. This means that we round up to
44.38. The area of the segment is 44.38
square centimeters.

As this is the area of the minor
segment, we could calculate the area of the major segment by subtracting this answer
from 227 square centimeters.