Find number of quadrilaterals

Let us first consider 1 quadrilateral In this figure, there is only $1$ quadrilateral

Let us consider 2 quadrilaterals In this figure there are $4$ quadrilaterals

Let us consider 3 quadrilaterals In this figure there are $9$ quadrilaterals.

Let us consider 4 quadrilaterals In this figure there are $16$ quadrilaterals.

Let us consider 5 quadrilaterals. In this figure there are $25$ quadrilaterals.

So, we observe, the number of quadrilaterals, in each case is the $square$ of the number of quadrilaterals on the same base. For example, in case 2, there are $2$ quadrilaterals on the same base. So, the total number of quadrilaterals are $2^2$ = $4$ .

So, in the given figure(question) there are 11 quadrilaterals on the same base. So, the total number of quadrilateral are $11^2$ = $121$ Hope you like the solution :-)

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There are 11 "candidate lines" on each side. We can easily see that we can only form a quadrilateral by choosing 1 candidate line from each side. Hence the total number of quadrilaterals is ${11\choose1} \times{11\choose1}=121$