Area of Circles with Exercises Geometry Regular Program SY 2015-2016 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? Half of circumference Rearrange the pieces to form a “paralellogram”.

Area of Circles and Parts

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:

Determine the area of the shaded region. 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 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.