This is a common difference question.

Take whole square area as 4 units.
Take whole rectangle area as 7 units.

Difference = 7 units - 4 units = 3 units


Unshaded area of square = 1 unit
Unshaded area of rectangle = 3 units

Difference = 3 units - 1 unit = 2 units


Now the shaded area is the same for both.


This also means :

Difference between the whole area of rectangle and whole area of square

= the difference between unshaded area of rectangle and unshaded area of square.

(Eg. Lets say

Shaded area = 3,
Whole rectangle area = 10
Whole square area = 8
Difference = 10 - 8 = 2

Now unshaded rectangle = 10 - 3 = 7
Unshaded square = 8 - 3 = 5
Difference = 7 - 5 = 2

Because to get the unshaded, we are removing the same shaded area from both. So the difference doesn't change)


From above, notice the difference is not the same yet.

So we need to change the units to make them the same.

The common multiple of 2 and 3 is 6.
(2 x 3 = 6, 3 x 2 = 6)


Multiply by 2,
Difference between rectangle and square's whole areas
= 14 units - 8 units = 6 units

Multiply by 3,
Difference between rectangle and square's unshaded areas
= 9 units - 3 units = 6 units


From above we see that shaded area

= 14 units - 9 units = 5 units
Or
= 8 units - 3 units = 5 units


5 units = 30cm²
1 unit = 30cm² ÷ 5 = 6cm²


Area of figure
= Unshaded square + unshaded rectangle + shaded area

= 9 units + 3 units + 5 units
= 17 units

= 17 x 6cm²
= 102cm²