Area of Circles with Exercises

Geometry Regular ProgramSY 2014-2015

Sources:

Discovering Geometry (2008) by Michael Serra

Geometry (2007) by Ron Larson

CIRCUMFERENCE vs. AREA

Imagine a string that will be wrapped around a coin, or wheel (without overlaps). The length of that string determines the circumference of the circular object.In any circle, the ratio Circumference over diameter is constant.

This ratio is known as pi.

Pi is equal to 3.14159265359…

How do we get the area of a circle?

A circle can be separated into smaller parts that resemble a “pizza slice”.

How do we get the area of a circle?

A circle can be separated into smaller parts that resemble a “pizza slice”.

How do we get the area of a circle?

Rearrange the pieces to form a “paralellogram”.

Half of circumference

Area of Circles and Parts

Area of Circles and Parts

Area of Circles and Parts

Area of Circles and Parts

• Example:

Area of Circles and Parts

• Example:

Area of Circles and Parts

• Example:

Area of Circles and Parts

Half of circumference

Determine the area of the shaded region.

Determine the area of the shaded region.

Determine the area of the shaded region.

Determine the area of the shaded region.

Determine the area of the shaded region.

Determine the area of the shaded region.

Determine the area of the shaded region.

Determine the area of the shaded region made up of semicircles.

Determine the area of the shaded region.The arcs are from a circle with radius of 6cm.The quadrilateral is a square.

Which shaded region has a greater area?

Determine the area of the shaded region.

Determine the area of the shaded region.

Determine the area of the shaded region.