Question

If mAB = 72 degree, find the area of shaded sector AOB, in terms of pi

Answer 1

If mAB = 72 degrees, then the central angle O will have the same measure.

Now, to find the sector area of a circle, we use the next equation:

$\frac{central\text{ angle}}{360}=\frac{sector}{\pi r^2}$

Where :

r = radius = 10

O = Central angle = 72 degrees.

Solve for the area of the sector AS:

$AS=\frac{central\text{ angle}}{360}\ast\pi r^2$

Replacing:

$AS=\frac{72}{360}\ast\pi(10)^2$

Solve it:

$AS=20\pi$

Hence, the area of the vector is 20π.