Question

PUZZLE The blocks that form the diagonals of each square are shaded. Each block has an area of one square unit. Find the “green area” of Square 20. Find the “green area” of Square 21.

Answer 1

The "green area" of Square 20 is 12 square units and the "green area" of Square 21 is 16 square units.

Step-by-step explanation:

Mathematics To find the "green area" of Square 20, we need to determine how many shaded blocks are in Square 20. Looking at the diagram or counting, we can see that Square 20 has 12 shaded blocks. Since each shaded block has an area of one square unit, the "green area" of Square 20 is 12 square units.
To find the "green area" of Square 21, we can use the same method. Looking at the diagram or counting, we can see that Square 21 has 16 shaded blocks. Therefore, the "green area" of Square 21 is 16 square units.
In summary, the "green area" of Square 20 is 12 square units and the "green area" of Square 21 is 16 square units.

Answer 2

Hi,

44 and 45

Step-by-step explanation:

I note n%2 the remainder of n divided by 2
and U(n) the number of green squares for the square n.

`u_1=5=4+1*2-1\%2\\u_2=8=4+2*2-2\%2\\u_3=9=4+3*2-3\%2\\u_4=12=4+4*2-4\%2\\u_5=4+5*2-5\%2\\...\\\\\boxed{u_n=4+n*2-n\%2}\\\\\\if\ n=20:\ 20\%2=0,\ u_(20)=4+20*2-20\%2=4+40-0=44\\\\if\ n=21:\ 21\%2=1,\ u_(21)=4+21*2-21\%2=4+42-1=45\\`