10.11. Area of Sectors and Segments http://www.ck12.org
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter10AreaofSectorsandSegmentsB
Concept Problem Revisited
The area of the crust for a deep-dish pizza is 8^2 π− 72 π= 15 π. The area of the crust of the thin crust pizza is
82 π− 7. 52 π=^314 π. One-twelfth of the deep dish pizza has^1512 πor^54 πin^2 of crust. One-fourth of the thin crust pizza
has^3116 πin^2. To compare the two measurements, it might be easier to put them both into decimals.^54 π≈ 3. 93 in^2
and^3116 π≈ 6. 09 in^2. From this, we see that one-fourth of the thin-crust pizza has more crust than one-twelfth of the
deep dish pizza.
Vocabulary
Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Aradiusis
the distance from the center to the outer rim of the circle. Achordis a line segment whose endpoints are on a circle.
Adiameteris a chord that passes through the center of the circle. The length of a diameter is two times the length
of a radius.Areais the amount of space inside a figure and is measured in square units.π, or“pi”is the ratio of the
circumference of a circle to its diameter. Asector of a circleis the area bounded by two radii and the arc between
the endpoints of the radii. Asegment of a circleis the area of a circle that is bounded by a chord and the arc with
the same endpoints as the chord.
Guided Practice
- The area of a sector is 135πand the arc measure is 216◦. What is the radius of the circle?
- Find the area of the shaded region. The quadrilateral is a square.
- Find the area of the blue sector of
⊙
A.
Answers:
- Plug in what you know to the sector area formula and solve forr.
135 π=216 ◦
360 ◦
·πr^2135 =3
5
·r^2
5
3· 135 =r^2225 =r^2 →r=√
225 = 15
- The radius of the circle is 16, which is also half of the diagonal of the square. So, the diagonal is 32 and the sides
would be√^32
2
·
√
√^2
2
= 16
√
2 because each half of a square is a 45-45-90 triangle.