In this picture the measure of angle theta is 1 radian

To solve this, we are going to use the formula for the area of the sector of a circle: 
where
is the area of the circular sector.
is the radius of the circle.
is the central angle in radians.

We know form our problem that that the measure of the central angle is 1 radian, so . We can also infer from the picture that the radius of the circle is 3in, so . Lets replace those values in our formula to find :




We can conclude that the area of the circular sector in the picture is 4.5 square inches.

To prove that the arc length is indeed 3 inches, we are going to use the formula: 
where
is the arc length.
us the radius of the circle.
is the central angle.

We know from our problem that , and , so lets replace those values in our formula:




We can conclude that the length of the arc is indeed 3 inches.

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