1. 10.7 Areas of Circles and Sectors
Learning Target:
I can find the area of circles, sectors, and segments.
10.7 Areas of Circles and Sectors

2. Area of a Sector
Sector of a Circle – region bounded by 2 radii and their intercepted arc

3. Ex. 1 Find the area of the sector. Leave in terms of .
360° =
• r2
90°
360° =
• (4)2
= 4  ft2

4. Ex. 2 Find the area of the sector. Leave in terms of .
360° =
• r2
315°
360° =
• (4)2
= 14 in2

5. Asegment = Asector - AΔ Area of a Segment
Segment of a Circle – Part of a circle bounded by an arc & the segment joining its endpoints.
Asegment = Asector - AΔ
Area of a Δ
A = ½ bh

6. Ex. 1: Find the area of the segment
Ex.1: Find the area of the segment. Round your answer to the nearest tenth. C
mABC = 90°
10cm
Trianlge Area
½bh
½(10)(10)
50cm2
Sector Area
= mARC
360 • r2
= 90
360 • (10)2
= 78.5 cm2 B
90 ° A
Segment Area = Sector Area- Triangle Area
= – 50
= cm2

7. Ex. 3: Find the area of the shaded region
Ex.3: Find the area of the shaded region. (note: you will add the sector area to the triangle area) Round your answer to the nearest tenth.
Trianlge Area
½bh
½(11)(11)
61cm2
Sector Area
= mARC
360 • r2
= 270
360 • (11)2
= cm2
Shaded Area = Sector Area + Triangle Area =
= cm2