Question

The floor plan of a ballroom is shown at right. The scale is 3 centimeters : 4 meters.

Answer 1

Given:
scale: 3 cm : 4 m
Length 12 cm
Width 9 cm

We 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 = 16 m * 12 m
Area = 192m²

Area in  cm: 12 cm * 9 cm
Area in cm: 108 cm²

cm : m ⇒ ratio format

ratio: a:b = c:d where ad = bc

108 : 192 = 12² : 16²
108 : 192 = 144 : 256

a = 108 ; b = 192 ; c = 144 ; d = 256

108 * 256 = 192 * 144
27,648 = 27,648