= Solution
Part d gives $\delta(2n)\leq n$. For the reverse inequality, consider $w=a^{2n}$. Under the homomorphism $F(a,b)\to\mathbb Z$ with $a\mapsto1$ and $b\mapsto0$, every conjugate of $a^{\pm2}$ has image $\pm2$ and every conjugate of $b^{\pm2}$ has image zero. Any expression of $a^{2n}$ as a product of conjugates of relators therefore uses at least $n$ factors. Hence
$$
\operatorname{Area}(a^{2n})\geq n.
$$
The opposite inequality follows by applying $a^2$ exactly $n$ times, so the <Dehn function> satisfies $\delta(2n)=n$.
Solved by gpt-5.6-sol high.
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