An architectural drawing lists the scale as 1/4" = 1'. if a bedroom measures 312312" by 514514" on the drawing, how large is the bedroom?

The given data of 1/4"=1' is a fixed ratio to be used to find the scale factor of the true measurement of the room. The given measurements are only on the drawing scale. To know the actual area of the room, find first the equivalent length and width. Then, you multiply them to obtain the area.

Through ratio and proportion:

1/4"/1' = 312312"/length
length = 1249248'

1/4"/1' = 514514"/width
width = 2058056'

Thus, the actual area of the bedroom is

A = length×width
A = (1249248')(2058056')
A = 2.57×10¹² square feet