The dimensions of a rectangular dining room are 18 feet by 16 feet. If a scale factor of One-fourth is used to make a scale model of the dining room, what is the area of the dining room in the scale model?
dimensions of scale model is 18/4 by 16/4
or 9/2 by 4
area = (9/2)(4) = 18 ft^2
since the area changess by the square of the scale factor, the new area is
(18*16)(1/4)^2 = 18 ft^2
18 ft^2
To find the area of the dining room in the scale model, we need to use the concept of scale factor.
1. Determine the scale factor: The scale factor given is one-fourth. It means that every measurement in the scale model is one-fourth of the corresponding measurement in the actual dining room.
2. Calculate the dimensions of the scale model: To find the dimensions of the scale model, we need to multiply the dimensions of the actual dining room by the scale factor.
Length of the scale model = Length of the dining room * Scale factor
= 18 feet * 1/4
= 4.5 feet
Width of the scale model = Width of the dining room * Scale factor
= 16 feet * 1/4
= 4 feet
3. Calculate the area of the scale model: The area of the scale model is simply the product of the length and width of the scale model.
Area of the scale model = Length of the scale model * Width of the scale model
= 4.5 feet * 4 feet
= 18 square feet
Therefore, the area of the dining room in the scale model is 18 square feet.