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Question

If the sum of the actual areas of the swings and the office in the map of a park shown below is 17100 sq. m, what is the scale used in the map? Take a unit square in the map as 1 cm × 1 cm.


A
1 cm = 10 m
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B
1 cm = 20 m
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C
1 cm = 30 m
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D
1 cm = 50 m
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Solution

The correct option is C 1 cm = 30 m
We can determine the area of each structure by counting the number of unit squares covered by them.

Area of swings in the map = 2 + 4 + 4 = 10 sq. cm
Area of the office in the map = 3 + 3 + 3 = 9 sq. cm

Total area in the map = 10 + 9 = 19 sq. cm

Given that the total area in actuality of the swings and the office to be 17100 sq. m, let's calculate the actaula area of a unit square in the map.

Actual area of a unit square in the map = 17100 ÷ 19 = 900 sq. m = 30 m × 30 m

Thus the scale used in the map is
1 cm = 30 m

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