Geometry 11.5Geometry 11.5Big Idea: Areas of Circles Big Idea: Areas of Circles

and Sectorsand Sectors

Theorem 11.9: Area of a CircleTheorem 11.9: Area of a Circle

Area equals pi times the square Area equals pi times the square of the radius.of the radius.

Example: Find the area.

Example: Find the radius.

Example: Find the diameter.

Vocabulary:

Sector: A region in a circle bounded by 2 radii and their intercepted arc.

Theorem 11.10: Area of a SectorTheorem 11.10: Area of a Sector

Area of a sector equals the Area of a sector equals the product of the entire circle area product of the entire circle area and the ratio of the intercepted and the ratio of the intercepted arc to 360arc to 360º.º.

Formula for Area of a Sector

Area of sector AOB =mAB πr2

360º

Example: Find the area of sector UTV.

Example: Find the area of sector FDE.