Illustrations in solving Arcs and Sector

3. Dear God,
thank you for looking after our school.
Thank you that you love each and every one of us here.
Help us to learn, play and share together.
It’s incredible that you are there every second of the day,
everywhere,
all the time,
beside each of us.
Amen.
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6. 𝐴 = 𝜋𝑟2
= 3.14 3𝑐𝑚 2
= 28.26𝑐𝑚2
𝐴 =
1
2
𝑏ℎ
=
1
2
8𝑐𝑚 6𝑐𝑚
= 24𝑐𝑚2
AREA OF THE CIRCLE AND TRIANGLE

7. TRIGONOMETRY
A =
1
2
𝑎𝑏𝑠𝑖𝑛𝐶
Where a, b are two sides and C
is the included angle.
A =
1
2
𝑎𝑏𝑠𝑖𝑛𝐶
=
1
2
4𝑚 4𝑚 𝑠𝑖𝑛80°
= 8𝑐𝑚2 0.984
= 7.87𝑐𝑚2

10. AREA OF THE
SECTOR AND
SEGMENT OF A
CIRCLE
Objectives
1. Define sector and segment of
the circle.
2. Find the area of the sector and
segment of a circle.
3. Appreciate the importance of
the lesson
:

11. SECTOR OF A CIRCLE- is the region bounded by an arc of
the circle and two radii to the endpoints of an arc.
The red portion is the sector of the circle. The bigger part
is the MAJOR SECTOR and the smaller part is the MINOR
SECTOR.
Area of a sector =
𝜃
360°
𝜋𝑟2
𝜃

12. SEGMENT OF A CIRCLE- is the region bounded by an
arc and the segment joining its endpoints.
The green portion is the segment of the circle.
Area of a segment = Asector - Atriangle

13. What is the area of the shaded portion?
Area of a sector =
𝜃
360°
𝜋𝑟2
=
60°
360°
𝜋(10𝑐𝑚)2
= 52.36 cm2

14. What is the area of the shaded portion?
Area of a segment = Asector - Atriangle
=
𝜃
360°
𝜋𝑟2 − 1
2
𝑏ℎ
= 7. 13 cm2

15. Area of a segment = Asector - Atriangle
=
𝜃
360°
𝜋𝑟2 -
1
2
𝑟2𝑠𝑖𝑛𝐶
=
1350
360°
(3.14)(8𝑐𝑚)2 -
1
2
(8𝑐𝑚)2𝑠𝑖𝑛1350
= 52.77cm2

17. What is the area of the shaded
portion?
Area of a sector =
𝜃
360°
𝜋𝑟2
=
60°
360°
𝜋(10𝑐𝑚)2
= 52.36 cm2

18. What is the area of the shaded
portion?
Area of a segment = Asector - Atriangle
=
𝜃
360°
𝜋𝑟2
− 1
2
𝑏ℎ
= 7. 13 cm2

19. Area of a segment = Asector - Atriangle
=
𝜃
360°
𝜋𝑟2 -
1
2
𝑟2𝑠𝑖𝑛𝐶
=
1350
360°
(3.14)(8𝑐𝑚)2
-
1
2
(8𝑐𝑚)2
𝑠𝑖𝑛1350
= 52.77cm2

20. Each group will draw 2 circles
with sector and segment of a
circle, and find the area of
sector and area of the segment
in each circle.

21. SCORE DESCRIPTORS
20 The circle is accurately made, presentable
and all answers are correct.
15 The circle is accurately made, but not
presentable and all answers are correct.
10 The circle is accurately made, presentable
but not all answers are correct.
5 The circle is accurately made, but not
presentable and not all answers are correct.

22. Find the area of the shaded portion.
1 2
3 4