SOLUTION: A region of a country is represented on a map of scale 1:25,000 by an a area of 11.5cm². Find the area of the region to the nearest hectare?

Question 1205081: A region of a country is represented on a map of scale 1:25,000 by an a area of 11.5cm². Find the area of the region to the nearest hectare?
Found 2 solutions by Theo, math_tutor2020:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe that this scale means that 1 centimeter on the map is equal to 25000 centimeters on the ground.

if the area on the map is equal to 11.5 square cm, then each side of the square is equal to sqrt(11.5) centimeters.

multiply sqrt(11.5) centimeters by 25000 to get an equivalent 84779.12479 centimeters on the ground.

square that to get an equivalent 7187500000 square centimeters on the ground.

1 hectare is equal to 10 ^ 8 square centimeters = 100,000,000 square centimeters.

divide 7187500000 square cm by 10^8 to get 71.875 hectares.

that would be roughly 72 hectares.

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

The linear scale is 1:25,000
It means 1 cm on paper represents 25,000 cm in the real world.

25000 cm = 25000/100 = 250 m
We divide by 100 since 100 cm = 1 m.

We can rewrite that linear scale to say
1 cm : 250 m

Square each part of the linear scale to get the area scale.
1^2 = 1
250^2 = 62,500

1 square cm on paper corresponds to 62,500 square meters in the real world.

11.5 square centimeters on paper corresponds to 11.5*62500 = 718,750 square meters in the real world.

1 hectare is defined to be a square of side 100 meters.
Meaning that 1 hectare = (100)^2 = 10,000 square meters

Divide by 10,000 to convert from square meters to hectares.
(718,750)/(10,000) = 71.875 hectares

That will then round to 72 hectares

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