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
To find the area of the scale model, we need to apply the scale factor to the dimensions of the dining room.
The scale factor is 1/4, which means that each length in the scale model will be 1/4 of the actual length.
So, the length of the scale model will be 18 x 1/4 = 4.5 feet.
And the width of the scale model will be 16 x 1/4 = 4 feet.
Now, we can find the area by multiplying the length and width of the scale model.
Area = 4.5 feet x 4 feet = 18 square feet.
Therefore, the area of the dining room in the scale model is 18 square feet, which is option A.
To find the area of the dining room in the scale model, we need to apply the scale factor of 1/4 to the dimensions of the dining room.
The dimensions of the dining room are 18 feet by 16 feet. To scale down these dimensions by 1/4, we multiply each dimension by the scale factor:
18 feet × 1/4 = 4.5 feet
16 feet × 1/4 = 4 feet
Now we have the dimensions of the scaled-down model, which are 4.5 feet by 4 feet.
To find the area of the scale model, we multiply the length and width of the model:
Area = length × width
= 4.5 feet × 4 feet
= 18 square feet
Therefore, the area of the dining room in the scale model is 18 square feet.
So, the correct answer is A. 18 square feet.
36
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