### Video Transcript

Write an expression for the area of
a sector whose arcβs measure is π radians, knowing that the expression for the area
of a sector measuring π degrees is ππ squared π over 360.

So weβre reminded of the formula we
can use to calculate the area of a sector when the central angle is given in
degrees. And weβre asked to use this to
determine a different formula we can use when the angle is given in radians. We should recall that when weβre
working in radians, a full turn, which in degrees is equivalent to 360 degrees, is
two π radians. So we can take the formula that we
know for the area of a sector in degrees, and we can replace the 360 in the
denominator, which represents the 360 degrees in a full turn with two π. Doing so gives ππ squared π over
two π. Now, of course, we can cancel a
factor of π from the numerator and denominator of this fraction, which leaves us
with π squared π over two or, equivalently, one-half π squared π.

So weβve used the area of a sector
in degrees to find an expression for the area of sector when the central angle is
given in radians; itβs one-half π square π.