Explanation

(a) Area $(A)$ covered by TV signal is given by
$A = \pi d^{2}$
Where $d$ is range given by
$d = \sqrt{2Rh}$
Where $R$ is radius of earth and $h$ the height of antenna.
$\therefore A = \pi(2Rh)$
Given, $A_{1} = A,\ A_{2} = 2A$
$\therefore\frac{A_{1}}{A_{2}} = \frac{h_{1}}{h_{2}}\ \Rightarrow \frac{h_{1}}{h_{2}} = \frac{1}{2}$
$\Rightarrow h_{2} = 2h_{1}$
Hence, height of transmitting antenna will have to be doubled.