thank you! :D

correct answer should be 180 cm2.

the mistake in this working is in the B and F. is the semi-circle on the right supposed to be just B alone, or B+F together?

the easier way to solve this problem is to use "cut-and-paste" and simplify the shape.
using the drawing as shown on the left here, we add one more line from the center of the square to the lower right corner of the square.
this divides B in the diagram into 2 portions, a right-angled isosceles triangle and a small shaded area (lets call it G) that is exactly the same shape and size as F.

we cut out shaded C and paste it into the unshaded area D.
we cut out shaded G and paste it into the unshaded area F.

you should now be able to see that the total shaded area is equivalent to (3/4) of the square. no need to involve any area of circle calculation.

total shaded area = (3/4)x240 = 180 cm2.

Shaded area = triangle ADF + semicircle B - F - F

Agree with Boy Mow Chau, should be 3/4 of the big square = 180 cm2. That is a brilliant solution. Thanks!

Thank you Boy Mow Chau for your comment :D

thank you :)