Question

1.) The island shown has a population of 12,175 people. Find the population

density in people per square kilometer.

18.5 km

11.1 km

Answer 1

Population density =
`148.22\ \text{people per square kilometer}`

Explanation:

The attached figure shows the dimension of an island.

Population density is equal to total population per unit land area.

Firstly we will find the area of the triangle using Pythagoras theorem as follows :

`H^2=B^2+P^2`

H is Hypotenuse, B is base and P is perpendicular

`B=√(H^2-P^2) \\\\B=√((18.5)^2-(11.1)^2) \\\\B=14.8\ km`

Area of triangle is given by :

`A=(1)/(2)* b* P\\\\A=(1)/(2)* 14.8* 11.1\\\\A=82.14\ km^2`

`\text{Population density}=\frac{\text{Total population}}{\text{land area}}\\\\=(12175 )/(82.14)\\\\=148.22\ \text{people per square kilometer}`

Hence, the population density is
`148.22\ \text{people per square kilometer}`.