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D = 12 cm42°Find the area of the green sector.

D = 12 cm42°Find the area of the green sector.-example-1

2 Answers

4 votes

Answer:

A ≈ 43.4 cm²

Explanation:

the area (A) of the green sector is calculated as

A = area of circle × fraction of circle

given d = 12 then r = 12 ÷ 2 = 6 cm

the central angle of the green sector = 180° - 42° = 138°

then

A = πr² ×
(138)/(360) ( simplify fraction by dividing numerator/denominator by 6 )

= π × 6² ×
(23)/(60)

= 36π ×
(23)/(60)

=
(36\\pi (23) )/(60)

≈ 43.4 cm² ( to the nearest tenth )

User Mamidon
by
7.8k points
3 votes

We will determine the area of the green section as follows:


A=r^2\cdot(\alpha)/(2)

Here alpha is the angle [In radians] and r is the radius-

*First: We determine the angle:


\alpha=360-42-180\Rightarrow\alpha=138

Now, we transform it to radians:


138\cdot(\pi)/(180)=(23)/(30)\pi

*Second: We replace on the equation:


A=(6)^2\cdot(((23)/(30)\pi))/(2)\Rightarrow A=(69)/(5)\pi

So, the area of the green sector is 69pi/5 square centimeters. [Approximately 43.4 square centimeters]

User AvL
by
8.2k points

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