Question

The dimensions of a rectangle dining room are 18 feet by 16 feet.If a scale factor of 1/4 is used to make a scale model of the dining room,what is the area of the dining room in the scale model?
A.18 square feet
B.36 square feet
C.48 square feet
D.72 square feet

Answer 1

area of room = 288 ft^2
areas of similar figures area proportional to the square of their sides

so the area of the model is (1/4)^2 or 1/16 of the original area = (1/16)(288)
= 18 ft^2

or

sides of the model:
length = (1/4)(18) = 4.5
width = (1/4)(16) = 4
area of model = 4(4.5) or 18 ft^2

Answer 2

36