a) number of squares is always 1 more than the figure number.

Figure 1 : 2 squares
Figure 2 : 3 squares
Figure 3 : 4 squares
Figure 4 : 5 squares

So for Figure 6, there are 7 squares.

b) number of circles = figure number x figure number

So for figure 10, number of circles
= 10 x 10
= 100

Number of squares = 10 + 1 = 11

Total = 100 + 11 = 111

c)

what we notice is that since

Squares = figure number x 1 + 1
Circles = figure number x figure number

Total = figure number x figure number + figure number x 1 + 1

= figure number x (figure number + 1) + 1


Eg. For figure 4,

Squares = 4 x 1 + 1 = 4 + 1 = 5
Circles = 4 x 4 = 16

Total = 4 x 4 + 4 x 1 + 1
= 4 x (4 + 1) + 1
= 4 x 5 + 1
= 20 + 1
= 21


So for 6481 total squares and circles,

6481 = figure number x (figure number + 1) + 1

Subtract 1 from both sides,

6480 = figure number x (figure number + 1)

Now 6480 = 80 x 81

So the answer is figure 80

Tip : when you have figured out that :

(figure number) x (figure number + 1) = total - 1 = 6480,

Realise that the two numbers are very close. The product is very close to the product of squaring either number.

You can do a smart guess by finding the square root of 6480 with your calculator, and then taking the rounded down or rounded up whole number.

√6480 ≈ 80.4984472

From this we know that one of the numbers should be 80 (round down) and the other is 81 (round up)

80 x 81 = 6480

This is very close to (and in fact between)

80 x 80 = 6400
and
81 x 81 = 6561