Answer:
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 = [tex]\sqrt{6(6-4)^3}[/tex]
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
