Step 1: Let the equal side be \(s\) and half of the base be \(k\). From the perimeter, \(2s+2k=32\), so \(s+k=16\). From the Pythagorean theorem using the altitude of 8, \(s^2=k^2+8^2\), which rearranges to \(s^2-k^2=64\).
Step 2: Factor the left side as a difference of squares: \((s-k)(s+k)=64\). Since \(s+k=16\), substitute to get \((s-k)(16)=64\), so \(s-k=4\).
Step 3: Solve the pair \(s+k=16\) and \(s-k=4\) by adding and subtracting: \(2s=20 \Rightarrow s=10\), and \(2k=12 \Rightarrow k=6\). So the base is \(2k=12\) cm.
Step 4: Compute the area: \( \text{Area} = \frac{1}{2}\times12\times8 = 48 \).
\[ \boxed{48 \text{ cm}^2} \]