You will find the areas of circles and composite

figures as well as find areas

of sectors.

Let’s look at some theorems.

10-11 Area of a Circle

The area of a circle is the product of π and

the square of the radius.

O

r A = π r ²

Example:

How much more pizza is in a 12-in-diameter pizza than in a 10-in. pizza?

r = 5

A = π(5)2

A = 25π

A = 36π – 25πA = 34.5 in2 more

r = 6

A = π(6)2

A = 36π

Here come more theorems.

10-12 AREA OF A SECTOR

THE AREA OF A SECTOR IS THE PRODUCT OF THE RATIO MEASURE OF THE

ARC AND THE AREA OF THE CIRCLE360

r

R

SO

A = m RS

360(πr²)

(

Example:Find the area of the sector of

the slice of pizza.

720

20 cm

A = m RS

360(πr²)

(

R

S

A = m 72

360(π20²)

(

A = 80π cm²A = 251.33 cm²

Here comes a term.Segment of a Circle

A part of a circle bounded by an arc and the segment joining its

endpoints.

Areaof sector – Areaof triangle = Areaof segment

R

SO

segment of a circle

EXAMPLE: Find the area of the shaded segment.

R

SO 10 in

A = m RS

360(πr²)

(

A = m 90

360(π10²)

(

A = 1/4 (100)πA = 25 π

A = 1/2 bhA = 1/2(10)(10)A = 1/2(100)A = 50

A = 25 π – 50 A = 28.53 in2

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