Answer – \[3256k{{m}^{2}}\]
There is no physical obstruction between the transmitter and the receiver antennae in case of the line-of-sight communication and hence there is no such requirement that the transmitting and receiving antennae should be at same height.
We are given,
Height of the antenna; h = 81 m
Radius of earth; R = 6.4 x 106m
We know that the service area of the antenna is given by the relation –
\[A\text{ }=\text{ }\pi {{d}^{2}}\]
Where d is the range given by the formula,
$d={{\left( 2\pi h \right)}^{\frac{1}{2}}}$
So, the formula of service area becomes –
$$ A=\pi \left( 2Rh \right) $$
$$ A=3.14\times 2\times 6.4\times {{10}^{6}}\times 81 $$
$$ A=3255.55\times {{10}^{6}}{{m}^{2}} $$
$$ A=3256k{{m}^{2}} $$