Question

Calculate the area of the larger sector if the length of the radius is 4.5

Answer 1

First take the area of the circle as a whole.

Answer 2

Ok, I got 63.59,
What's the next step?

Answer 3

Alright, so observe the enclosed graphic. Notice how when we bisect the circle, we get a new angle of 10 degrees. Why? Because a semi circle is 180 degrees, the old angle was 190; \(190 - 180 = 10\). OK, so first divide the area by 2. Now, we have to add the area of the triangle we just made (see graphic). We know the hypotenuse, which is 4.5. We know the angle. This is sufficient to find the area. The following equation is the area of the triangle:
$$A = \frac{1}{2}(\sin(10 deg) 4.5)$$
Now, add this to the area of the circle divided by 2.