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 $\times$ 1 cm.

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

Answer 1

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 $\times$ 30 m

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