Question

The area of a square floor on a scale drawing is 36 square cm, and the scale drawing is 1cm:4ft. what is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?

Answer 1

Part a) The area of the actual floor is
`576\ ft^(2)`

Part b) The ratio of the area in the drawing to the actual area is
`(1)/(16)(cm^(2))/(ft^(2))`

Explanation:

step 1

Find the length of the square floor on a scale drawing

Let

b-----> the length side of the square floor on a scale drawing

we know that

`A=b^(2)`

we have

`A=36\ cm^(2)`

`36=b^(2)`

`b=6\ cm`

step 2

Find the length of the square floor in the actual floor

we know that

the scale drawing is
`1cm:4ft`

so

the length of the square floor in the actual floor is equal to

`6*4=24\ ft`

step 3

Find the area of the actual floor

`A=24^(2)=576\ ft^(2)`

step 4

Find the ratio of the area in the drawing to the actual area

`(36)/(576)(cm^(2))/(ft^(2))`

simplify

`(1)/(16)(cm^(2))/(ft^(2))`