ISEE Upper Level Math : How to find the area of a sector

Example Questions

Example Question #1 : How To Find The Area Of A Sector

Give the area of the white region of the above circle if  has length

Explanation:

If we let  be the circumference of the circle, then the length of  is  of the circumference, so

The radius is the circumference divided by :

Use the formula to find the area of the entire circle:

The area of the white region is  of that of the circle, or

Example Question #2 : How To Find The Area Of A Sector

The circumference of the above circle is . Give the area of the shaded region.

Explanation:

The radius of a circle is found by dividing the circumference  by :

The area of the entire circle can be found by substituting for  in the formula:

.

The area of the shaded  sector is  of the total area:

Example Question #3 : How To Find The Area Of A Sector

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the area of the highlighted wedge?