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One other visual approach independent of $n$ ($n=10$ here)

The biggest one of both areas (white in OP case) can be seen as sum of $n$ areas (colored red green alternating top down here) each one equal to $k$ $(1<=k<=n)$ units. One unit being the 'top' triangle area.

But then that area equals (by Gauss formula): $n*(n+1)/2$, in this case: $55$

Similarly smallest one (grey in OP case, but not given a color here) has area: $n*(n-1)/2$, in this case: $45$

As a consequence this also confirms:

Total area equals $n^2$ units, in this case: $100$ giving both percentages $45$ and $55$.

Required percentages for any $n$ now are easy to express in terms of above for any $n$.

One other visual approach independent of $n$ ($n=10$ here)

The biggest one of both areas (white in OP case) can be seen as sum of $n$ areas (colored red green alternating top down here) each one equal to $k$ $(1<=k<=n)$ units. One unit being the 'top' triangle area.

But then that area equals (by Gauss formula): $n*(n+1)/2$, in this case: $55$

Similarly smallest one (grey in OP case, but not given a color here) has area: $n*(n-1)/2$, in this case: $45$

As a consequence this also confirms:

Total area equals $n^2$ units, in this case: $100$ giving both percentages $45$ and $55$.

Required percentages for any $n$ now are easy to express in terms of above for any $n$.

One other visual approach independent of $n$ ($n=10$ here)

The biggest one of both areas (white in OP case) can be seen as sum of $n$ areas (colored red green alternating top down here) each one equal to $k$ $(1<=k<=n)$ units. One unit being the 'top' triangle area.

But then that area equals (by Gauss formula): $n*(n+1)/2$, in this case: $55$

Similarly smallest one (grey in OP case, but not given a color here) has area: $n*(n-1)/2$, in this case: $45$

As a consequence this also confirms:

Total area equals $n^2$ units, in this case: $100$.

Required percentages now are easy to express in terms of above for any $n$.

One other visual approach independent of $n$ ($n=10$ here)

The biggest one of both areas (white in OP case) can be seen as sum of $n$ areas (colored red green alternating top down here) each one equal to $k$ $(1<=k<=n)$ units. One unit being the 'top' triangle area.

But then that area equals (by Gauss formula): $n*(n+1)/2$, in this case: $55$

Similarly smallest one (grey in OP case, but not given a color here) has area: $n*(n-1)/2$, in this case: $45$

As a consequence this also confirms:

Total area equals $n^2$ units, in this case: $100$ giving both percentages $45$ and $55$.

Required percentages for any $n$ now are easy to express in terms of above for any $n$.

One other visual approach independent of $n$ ($n=10$ here)

The biggest one of both areas (white in OP case) can be seen as sum of $n$ areas (colored red green alternating top down here) each one equal to $1<=k<=n$ units. One unit being the 'top' triangle area.

But then that area equals (by Gauss formula): $n*(n+1)/2$, in this case: $55$

Similarly smallest one (grey in OP case, but not given a color here) has area: $n*(n-1)/2$, in this case: $45$

As a consequence this also confirms:

Total area equals $n^2$ units, in this case: $100$.

Required percentages now are easy to express in terms of above for any $n$.

One other visual approach independent of $n$ ($n=10$ here)

The biggest one of both areas (white in OP case) can be seen as sum of $n$ areas (colored red green alternating top down here) each one equal to $k$ $(1<=k<=n)$ units. One unit being the 'top' triangle area.

But then that area equals (by Gauss formula): $n*(n+1)/2$, in this case: $55$

Similarly smallest one (grey in OP case, but not given a color here) has area: $n*(n-1)/2$, in this case: $45$

As a consequence this also confirms:

Total area equals $n^2$ units, in this case: $100$.

Required percentages now are easy to express in terms of above for any $n$.