Question

Circle A has a radius of 12 in., m( arc BC )=π/6, m( arc CD ) = π/4. What is the area of the sector with the central angle ∠BAD?

Answer 1

Area of the sector = 94.25 in²

Explanation:

From the picture attached,

Length of the radius of the circle = 12 in.

m(arc BC) =
`(\pi )/(6)`

m(arc CD) =
`(\pi )/(4)`

Therefore, m(arc BD) = m(arc BC) + m(arc CD)

m(arc BD) =
`(\pi )/(6)+(\pi )/(4)`

=
`(5\pi )/(12)`

Since, area of a sector with central angle 'θ' is given by,

Area of the sector =
`(\theta)/(2\pi )(\pi r^2)`

By substituting the measures in the given formula,

Area of sector BAD =
`((5\pi )/(12))/(2\pi )(\pi )(12)^2`

=
`(5)/(24)(\pi )(144)`

=
`30\pi`

= 94.25 in²