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Answer:
Shaded area = 6^2 * ( pi/3 - sqrt(3)/2 )
= 6.52 square units (to 2 places of decimals)
Step-by-step explanation:
see solution by same author given in
brainly.com/question/17023327?answeringSource=feedPersonal%2FhomePage%2F2
(question 17023327)
Please refer to the diagram for additional letters and measures.
Let
r=radius (OA and PA) of each circle
Area of sector PAOB
= (60+60)/360 * pi * r^2
=pi*(r^2)/3
Area of triangle PAB
= 2* (r cos(60) * r sin(60) /2)
= 2* ((r/2) * r (sqrt(3)/2) /2)
= sqrt(3) * r^2 / 4
= r^2 * sqrt(3)/4
Area of segment AOB
= area of segment PAOB - area of triangle PAB
= r^2 * ( pi/3 - sqrt(3)/4 )
By symmetry, area of shaded area
= area of segment AOB - area of triangle AOB
= area of segment AOB - area of triangle PAB
= r^2 * ( pi/3 - sqrt(3)/4 ) - r^2 * ( sqrt(3)/4)
= r^2 * ( pi/3 - 2*sqrt(3)/4 )
= r^2 * ( pi/3 - sqrt(3)/2 )
Since r = b, we substitute
Shaded area
= b^2 * ( pi/3 - sqrt(3)/2 )
Substitute b=6
area
= 6^2 * ( pi/3 - sqrt(3)/2 )
= 6.522197 square units
