The areas of the two shaded regions are equal to each other.
Draw a line between the two vertices defining the lower-left region,
splitting it into two congruent regions. Now, imagine rotating the
upper-left portion by 90 degrees clockwise and the lower-left portion by
90 degrees counterclockwise, so that these regions now each abut the
upper-right crescent. Now the entire shaded region is a 2x magnified
(so it has 4x the area) version of either of the subregions of the
original lower-left region. Therefore, the area of all the shaded regions
together is twice the area of the original lower-left region, so
the two shaded regions have equal area.