Following pls find my worked solution (with reference to your attached question & figure ):
Given that 1/5 of triangle is shaded (ST), then 4/5 of triangle is Unshaded (UT). Likewise, if 2/7 of rectangle is shaded (SR), then 5/7 of rectangle is unshaded (UR).
We can express these as ratios (as shown):
** - buffer space for alignment purpose
UT : ST/SR : UR
4 * : ** 1
******* 2 ** : 5
Using <Repeated Identity> concept, we need to multiply 1st ratio 2x, as area of ST = area of SR. So we have ...
8 * : ** 2 ** : 5
Whole figure = 8u + 2u + 5u = 15u
Fraction of Whole figure shaded = 2/15
Given area of the shaded part is 28 cm2, we have ..
2u --> 28
1u --> 14
Total area of figure = 15u --> 15 x 14 = 210 cm2
Trust the above helps.
Do let me know again if this does not match your Answerkey or if there's any clarification.