A television tower is 180 m tall. A receiving antenna stands 20 m above the ground…

Step 1. The tower. $d = \sqrt{2 \times 6.4 \times 10^{6}\ \text{m} \times 180\ \text{m}} = 48000\ \text{m} = 48.0\ \text{km}$.

Step 2. The antenna. $d_r = \sqrt{2 \times 6.4 \times 10^{6}\ \text{m} \times 20\ \text{m}} = 16.0\ \text{km}$. The two horizons meet at the greatest distance, $48.0 + 16.0 = 64.0\ \text{km}$.

Step 3. The area. $\pi d^2 = \pi \times (48.0\ \text{km})^2 = 7.2 \times 10^{3}\ \text{km}^2$.

Step 4. A taller tower. $h = 720$ m gives $d = \sqrt{2 \times 6.4 \times 10^{6}\ \text{m} \times 720\ \text{m}} = 96.0\ \text{km}$, twice the first distance.