Question

the scale on a map is 1:20000. the area of a lake on the map is 1.6 square centimetres. Calculate the actual area of the lake. give your answer in square metres

Answer 1

32000 cm Square is the area

Answer 2

Answer:

Step-by-step explanation:

The puzzle here is obviously converting the observed measurement "1.6 sq centimeters" to the real measurement (final answer = 640 million sq centimeters), but you have to understand converting "square" measurements isn't the same as converting normal "linear" measurements i.e just 1.6 centimeters, we have to unravel the square measurement to its linear components first.

Thankfully this is super easy, take the 1.6 square centimeters and sq root it on a calculator. Done! Answer = 1.264911064cm, which means the area of the lake is approx. 1.265cm x 1.265cm, using its linear measurements.

And that's it! Just use the ratio of 1:20,000, which means 1 unit on the map (observed), is really 20,000 units in real life - real measurements are 20,000 times bigger than any observed one.

So, the 1.264911064cm lake measurement we multiply by 20,000, to give us 25,298.22128cm in real life, however we want the square area, so we square this number to give us 640,000,000 sq cm or 64,000 sq meters.  

(Extra: we have to divide the sq cm answer by 10^4 to get the answer in sq meters, you can check this by going back to the real linear measurement for the lake of 25,298.22128cm, converting it to meters the normal way - divide by 100, and then squaring that answer = 64,000 sq m, the normal cm to m scale factor 100 also squares to 10^4, now that we are dealing with "sq" cm and "sq" m )