Transcript Area of Circles and Sectors

Area of Circles and
Sectors
Lesson 7.4A
M.3.G.1 Calculate probabilities arising in geometric contexts (Ex. Find the probability of hitting a
particular ring on a dartboard.)
M.3.G.2 Apply, using appropriate units, appropriate formulas (area, perimeter, surface area,
volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders,
spheres as well as composite figures, expressing solutions in both exact and approximate forms
M.3.G.3 Relate changes in the measurement of one attribute of an object to changes in other
attributes (Ex. How does changing the radius or height of a cylinder affect its surface area or
volume?)
R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords,
tangents, and secants to solve problems involving circles
Area of Circles

Formula for area of a circle:
A
=
2
πr
Example

Find the area of the given circle.
18mm
Example

Given the endpoints of the diameter of
a circle, find the area of the circle.
Give your answer in terms of π.

STEPS: 1. Use the distance formula to find
the length of the diameter.
 2. Halve the diameter to find the
radius.
3. Use the radius to find the area
Example
Given the endpoints of the diameter of
a circle, find the area of the circle.
Give your answer in terms of π.
Endpoints of the diameter are: (7, -3) and (-1, 12)

Now You Try…
Given the endpoints of the diameter of
a circle, find the area of the circle.
Give your answer in terms of π.
 Endpoints of the diameter: (10, 12) and (5, 24)

Example
Given the circumference of a circle,
find the area of the circle. Give your
answer in terms of π and rounded to
the nearest hundredth.
 Circumference = 18 π miles

Now You Try…
Given the circumference of a circle,
find the area of the circle. Give your
answer in terms of π and rounded to
the nearest hundredth.
 Circumference = 389.56 inches

Comparing Radii and Areas

The radius of circle N is 3 times larger
than the radius of circle P. Describe
how the areas of the two circles
compare.
Vocabulary
Central Angle: An angle made by two
radii
 Arc: An unbroken part of a circle
 Sector: A region bounded by a central
angle and its intercepted arc
 Chord: A segment whose endpoints lie
on the circle
 Segment: A region bounded by a
chord and its intercepted arc

Sector Area

Formula for area of a sector:
 M  2
SectorArea 
  r
 360
Example

Find the area of the shaded sector.
Give your answer in terms of π and
rounded to the nearest tenth.
72
3 cm
Now You Try…

Find the area of the shaded sector.
Give your answer in terms of π and
rounded to the nearest tenth.
7 cm
Area of Segments

Find the area of the shaded segment.
Round your answer to the nearest
tenth.
-
=
4 ft
Now You Try…

Find the area of the shaded segment.
Round your answer to the nearest
tenth.
9 inches