1. **Problem:** Given a rectangle with diagonal $c=13$ cm and height $h=8$ cm, find the area $A$. 2. **Formula:** For a rectangle, area $A = \text{length} \times \text{height}$. The diagonal relates length $l$ and height $h$ by the Pythagorean theorem: $$c^2 = l^2 + h^2$$ 3. **Step 1:** Use the Pythagorean theorem to find length $l$: $$13^2 = l^2 + 8^2$$ $$169 = l^2 + 64$$ $$l^2 = 169 - 64 = 105$$ $$l = \sqrt{105}$$ 4. **Step 2:** Calculate the area: $$A = l \times h = \sqrt{105} \times 8 = 8\sqrt{105}$$ 5. **Step 3:** Approximate the area: $$\sqrt{105} \approx 10.247$$ $$A \approx 8 \times 10.247 = 81.976$$ cm$^2$ **Final answer:** The area of the rectangle is approximately $81.98$ cm$^2$.