Question

A catchment area consists of a square of side 4 km and a semicircle of 4 km diameter as shown below.


If the rainfall values at these stations are $P_1=15cm,P_2=25m,P_3=30cmand{P}_4=20cm$. The average rainfall over the basin by the thiessen polygon method would be____cm (up to 1 decimal place).

• A. 23.9

Answer 1

The correct option is A 23.9

$A_1=A_4=\frac{1}{4}\times \{4\times 4\}=\frac{16}{4}=4k{m}^2$

$A_2=A_3=\frac{1}{4}\times \{4\times 4\}+\frac{1}{4}\left[\frac{\pi \times 4^2}{4}\right]=4+3.142=7.142k{m}^2$


$P_a=\frac{(15\times 4)+(25\times 7.142)+(30\times 7.142)+(20\times 4)}{4+7.142+7.142+4}$

$P_a=23.9cm$