Step 1: Name the parts of the statement.
Let $p$: the two triangles are congruent, and $q$: their areas are equal. The original statement reads $p\rightarrow q$.
Step 2: Recall the inverse rule.
The inverse of $p\rightarrow q$ negates both sides without swapping, giving $\sim p\rightarrow\sim q$.
Step 3: Write the inverse explicitly.
So the inverse is $\sim p\rightarrow\sim q$, that is, if the triangles are not congruent then their areas are not equal.
Step 4: Recall the contrapositive rule.
The contrapositive of any conditional $A\rightarrow B$ is $\sim B\rightarrow\sim A$, swapping the two parts and negating each.
Step 5: Apply it to the inverse.
Treating the inverse as $A\rightarrow B$ with $A=\sim p$ and $B=\sim q$, its contrapositive is $\sim(\sim q)\rightarrow\sim(\sim p)$. Using double negation, $\sim(\sim q)=q$ and $\sim(\sim p)=p$, so this is simply $q\rightarrow p$.
Step 6: Translate back to words.
The statement $q\rightarrow p$ reads: if areas of two triangles are equal, then they are congruent. That is option (3).
\[ \boxed{q\rightarrow p:\ \text{equal areas} \Rightarrow \text{congruent}} \]