Question

On a map the scale is shown 1 inch : 3 miles if an island is 0.5 square inches on the map what the actual area of the island

Answer 1

4.5 square miles.

Explanation:

Silly method: the island being 0.5 square inches means it covers a rectangle which is 1 inch long and 0.5 wide. That means in reality it is 3 miles long and 1.5 miles wide, or that it covers 4.5 square miles.

Rigorous method: if two figures (geometric shapes, maps, etc) are in scale, it means that the the ratio of the surface is the square of the ratio of the linear measures (and volumes are the cube, but that's just extra trivia). In our case, you get
`0.5 in^2 * ((3 mi)/(1 in))^2 = 0.5* 9 mi^2 = 4.5 mi^2`