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shaded area = b^2 * ( pi/3 - sqrt(3)/2 )

Step-by-step explanation:

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 )

step-by-step explanation:

consider an orange peel: if you want to try and lay it flat, you have to stretch it, we know exactly how things are being stretched or squashed at any given point. we have many different map projections because each has different patterns of some projections can even preserve certain features of the earth without