The answer key is wrong because it has double-counted for the overlapping parts as seen in my diagram above.  The figure is made up of the 3 shapes overlapping at the shaded areas so it should be 27u instead of 33u..   hence my solution as follows still holds:

Square         Triangle         Rectangle          Total

        5u                8u                    20u                   33u

1/5 x 20u = 4u  = right shaded part of triangle

Total shaded part of triangle = 3/4 x 8u = 6u     =>     Unshaded part = 8u-6u = 2u

Hence total figure taking away the overlapping parts = 33u – 6u = 27u   or  5u+2u+20u = 27u

Fraction of shaded part of the figure = Shaded overlapping parts/ total figure

                                                                    =  6u/27u = 2/9

The answer key is wrong because it has double-counted for the overlapping parts as seen in my diagram above.  The figure is made up of the 3 shapes overlapping at the shaded areas so it should be 27u instead of 33u..   hence my solution as follows still holds:

Square         Triangle         Rectangle          Total

        5u                8u                    20u                   33u

1/5 x 20u = 4u  = right shaded part of triangle

Total shaded part of triangle = 3/4 x 8u = 6u     =>     Unshaded part = 8u-6u = 2u

Hence total figure taking away the overlapping parts = 33u – 6u = 27u   or  5u+2u+20u = 27u

Fraction of shaded part of the figure = Shaded overlapping parts/ total figure

                                                                    =  6u/27u = 2/9