1. 11.5 Areas of Circles and Sectors
Hubarth
Geometry

2. . Theorem 11.9 Area of a Circle
The area of a circle is 𝜋 times the square of the radius. . r
𝐴=𝜋 𝑟 2

3. a. Area r = 2.5 cm A = 113.1 cm2 b. Diameter A = πr2 A = πr2
Ex 1 Use the Formula for Area of a Circle
Find the indicated measure.
a. Area
r = 2.5 cm
A = cm2
b. Diameter
A = πr2
A = πr2
= π (2.5)2
= πr2
= 6.25π
= r2
113.1 π
A ≈ 19.63
r ≈ 6
D =12

4. . Theorem 11.10 Area of a Sector
The ratio of the area of a sector of a circle to the area of the whole circle (𝜋 𝑟 2 ) is equal
To the ratio of the measure of the intercepted arc to 360.
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟 𝐴𝑃𝐵 𝜋 𝑟 2 = 𝑚 𝐴𝐵 360 , or Area of sector APB= 𝑚 𝐴𝐵 360 ∙𝜋 𝑟 2 A r . P B

5. ≈ 39.10 ≈ 161.97 Ex 2 Find Areas of Sectors
Find the areas of the sectors formed by ∠UTV.
Find the measures of the minor and major arcs.
Because m ∠UTV = 70°, m 𝑈𝑉 = 70° and
m 𝑈𝑆𝑉 = 360° – 70° = 290°.
Area of small sector = 𝑚 𝑈𝑉 360 ∙𝜋 𝑟 2
Area of large sector = 𝑚 𝑈𝑆𝑉 360 ∙𝜋 𝑟 2
= ∙𝜋 (8) 2
∙𝜋 (8) 2
≈ 39.10 ≈

6. Ex 3 Use the Area of a Sector Theorem
Use the diagram to find the area of ⊙V.
Area of sector TVU= 𝑚 𝑇𝑈 360 ∙𝐴𝑟𝑒𝑎 𝑜𝑓 ⊙𝑉
35= ∙𝑎𝑟𝑒𝑎 𝑜𝑓 ⊙𝑉
𝑎𝑟𝑒𝑎 𝑜𝑓 ⊙𝑉=315

7. Ex 4 Standardized Test Practice
The area you need to paint is the area of the rectangle minus the area of the entrance. The entrance can be divided into a semicircle and a square.
180°
= (26) – (π ) + 162
360°
= 936 – [32π ] ≈
The correct answer is C.

8. Practice
Use the diagram to find the indicated measure.
1. Area of D
ft2
2. Area of red sector
ft2
3. Area of blue sector
ft2
4. Find the area o f H.
5. Find the area of the figure.
43.74 m2
cm2