Find the area of the shaded regions below. give your answer as a completely simplified exact value in terms of π (no approximations).

area of the shaded portion COA = 9.83 cm² = 3.128π cm²

area of the shaded portion COB = 1.442 cm² =0.459π cm²

in total= 9.83 + 1.442 = 11.27 cm² =  3.58π cm²

Step-by-step explanation:

area of sector of circle COB can be gotten by knowing the angle <COB

to calculate for the angle, we will use the three side of triangle given.

CO = 4cm, CB= 4cm and OB = 4 cm

cos θ = (OB/2)/OC =2/4 = 0.5

θ = 60 degree

since the three side are equal, that mean the triangle is equilateral

area of a sector = θ/360 * πr²

        =60/360 * π * 4 *4

       =  8.37 cm²

area of triangle COB

s = 4+4+4)/2 = 12/2 = 6cm

A =

A = 6.928 cm²

area of the shaded portion COB = area of sector - area of triangle

        = 8.37 cm² - 6.928 cm²  ==1.442 cm²

area of sector of circle COA can be gotten by knowing the angle <COA

to calculate for the angle, we will subtract 60 from 180 = 120.

θ = 120 degree

since the two side are equal, that mean the triangle is isosceles

area of a sector = θ/360 * πr²

        =120/360 * π * 4 *4

       =  16.76 cm²

area of triangle COA

    = 0.5 * 4 * 4* sine 120

    A = 6.928 cm²

area of the shaded portion COA = area of sector - area of triangle

        = 16.76 cm² - 6.928 cm²  ==9.83 cm²

area of the shaded portion COA = 9.83 cm² = 3.128π cm²

area of the shaded portion COB = 1.442 cm² =0.459π cm²

in total= 9.83 + 1.442 = 11.27 cm² =  3.58π cm²

you are saying it as if a fact, not a question, but yes, you would be correct? ; )

step-by-step explanation:

step-by-step explanation:

answers available in this download

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