If you subtract the area of the small quadrant from the area of the big one,

you are left with :

① The shaded portion of the big quadrant
② Its remaining unshaded portion that is inside the rectangle on the right.

Big quadrant's area
= ¼ x 3.14 x 20cm x 20cm
= 314cm²

Small quadrant's area
= ¼ x 3.14 x 10cm x 10cm
= 78.5cm²

314cm² - 78.5cm² = 235.5cm²


Now,

Notice that the rectangle on the right has a breadth of 10cm and length of 20 cm :

① Its length is equal to the big quadrant's radius of 20cm.

② Its breadth is equal to the radius of the big quadrant minus the radius of the small quadrant (20cm - 10cm = 10cm)



Next, subtract the area of the rectangle from the remaining area above.

By doing this we are removing the remaining unshaded portion inside the big quadrant, leaving us with the shaded portion. We are also subtracting the value of other shaded area (outside the quadrant, inside the rectangle)

This gives us our required difference.

(shaded area in the big quadrant - shaded area outside it)

Area of rectangle = 10cm x 20cm
= 200cm²

Difference in shaded areas

= 235.5cm² - 200cm²
= 35.5cm²

Visualisation in a form of an equation :


Shaded area inside big quadrant

= Area of big quadrant - area of small quadrant - unshaded area inside rectangle

Shaded area outside

= area of rectangle - unshaded area inside rectangle.

So,

Shaded area inside big quadrant - shaded area outside

= Area of big quadrant - area of small quadrant - unshaded area inside rectangle

- (area of rectangle - unshaded area inside rectangle)


= Area of big quadrant - area of small quadrant - unshaded area inside rectangle - area of rectangle + unshaded area inside rectangle

= Area of big quadrant - area if small quadrant - area of rectangle


Notice the 2 'unshaded area inside rectangle' s cancel out.