"Geometrical Properties of Quarter Circle
'<hr /><div style="max-width:120mm"><img style="height:120pt;" alt="quarter-circle.png" class="side" src="https://calcpad.eu/media/mechanics/sections/quarter-circle.png"></div>
'Radius -'r = ?'%u
'Area
A = π*r^2/4'%u<sup>2</sup>
'Centroid
'<p><i>z</i><sub>c</sub> ='y_c = 4*r/(3*π)'%u</p>
'Perimeter
P = (π/2+2)*r'%u
'Second moments of area
'<p><i>I</i><sub>z</sub> ='I_y = (π/16 - 4/(9*π))*r^4'%u<sup>4</sup></p>
I_yz = (1/8 - 4/(9*π))*r^4'%u<sup>4</sup></p>
'Principal area moments
I_1 = I_y + abs(I_yz)'%u<sup>4</sup>
I_2 = I_y - abs(I_yz)'%u<sup>4</sup>
'Angle of principal axis
α_1 = atan((I_y - I_1)/I_yz)'<sup>о</sup>
'Polar moment of area
I_x = 2*I_y'%u<sup>4</sup>
'Radii of gyration
'<p><i>r</i><sub>z</sub> ='r_y = sqr(I_y/A)'%u</p>
r_1 = sqr(I_1/A)'%u
r_2 = sqr(I_2/A)'%u
r_x = sqr(I_x/A)'%u1