Fibonacci sequence??? Seriously what are the teachers thinking..

The 14cm by 14 cm square has the same length as the two smallest squares combined.

Those two squares are identical as they have the same length. So each of their lengths = 14cm ÷ 2 = 7cm

Now, the bottom corner square has the same length as the sum of the lengths of the 1 smallest square and the 14-cm square.

So that square's length = 14cm + 7cm
= 21cm

Now the top corner square has the same length as the sum of the lengths of the 14-cm square and the 21-cm square.

So that square's length = 14cm + 21cm
= 35cm


And lastly, the rightmost square where the quadrant is in has the same length as the
sum of the lengths of the 21-cm square and the 35-cm square.


So that square's length = 21cm + 35cm
= 56cm

This length is equal to the radius of the quadrant.

So area of shaded quadrant
= ¼ x 22/7 x 56cm x 56cm
= 2464cm²


Additional info :


Ratio of the square lengths from smallest to biggest

= 1 : 2 : 3 : 5 : 8

This actually forms part of the Fibonacci sequence, which occurs in nature