Following is the measurement of projection area shown in post.

GeoArea (m^2)
with_ball_small0.01551
with_cone_long0.01380
with_cone_mid0.02029
with_cone0.02029
with_cylinder_longest0.01999
with_cylinder_longer0.01936
with_cylinder0.01761
with_ball_round0.01778
with_ball0.02566
lev_c0.00649
lev_b0.00650
lev_a0.00740