The floor plan of a ballroom is shown at right. the scale is 3 centimeters : 4 meters. what are the length and width of the ballroom? find the ballroom's area.
( the right is 12 cm as length and 9 cm as the width )

Area is 108 cm^2
Area is 192 m^2
Length is 16m
Width is 12m

You need to convert cm to m

length: (12cm/3cm) * (4m) = 4 * 4m = 16 meters

width: (9cm/3cm) * (4m) = 3 * 4m = 12 meters

Area = length * width
Area = 16m * 12m
Area: 192m^2, which is meters squared.

Area in cm: 12 cm * 9 cm

Area in cm: 108 cm

To verify:
The centemeter to meter ratio format is a:b and c:d
where
ad = bc

108 : 192 and 12^2 : 16^2

108 : 192 and 144 : 256

Where:
a = 108
b = 192
c = 144
d = 256

108 * 256 = 192 * 144
27,648 - 27,648
So the answer checks out!