Question

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

Answer 1

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 )

Answer 2

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]