Question

The area of a square floor on a scale drawing is 64 square centimeters, and the scale drawing is 1 centimeter:3 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area? The area of the actual floor is square feet. The ratio of the area in the drawing to the actual area is 1 square centimeter: square feet.

Answer 1

To find the area of the actual floor, multiply the side length of the square in the drawing by the scale factor and convert the units. The area of the actual floor is 576 square feet. The ratio of the area in the drawing to the actual area is 1 square centimeter: square feet.

Step-by-step explanation:

To find the area of the actual floor, we need to determine the dimensions of the actual floor. The scale of the drawing is 1 centimeter:3 ft, which means 1 centimeter in the drawing represents 3 feet in reality.

Since the area of the square floor in the drawing is 64 square centimeters, we know that the side length of the square in the drawing is 8 centimeters (since 8 x 8 = 64).

To find the side length of the actual square floor, we need to convert the scale to feet and multiply by the side length in the drawing:

1 centimeter × (3 ft/1 centimeter) × 8 centimeters = 24 feet.

Therefore, the area of the actual floor is 24 feet × 24 feet = 576 square feet.

The ratio of the area in the drawing to the actual area is 1 square centimeter: square feet.

Answer 2

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)/(9)(cm^(2))/(ft^(2))`

Step-by-step explanation:

we know that

The scale drawing is
`(1)/(3)(cm)/(ft)`

step 1

Find the dimensions of the square on a scale drawing

The area of a square is equal to

`A=b^(2)`

where

b is the length side of the square

`A=64\ cm^(2)`

so

`64=b^(2)`

`b=8\ cm`

step 2

Find the dimensions of the actual floor

Divide the length of the floor on the drawing by the scale drawing

`8/(1/3)=24\ ft`

step 3

Find the area of the actual floor

The area of a square is equal to

`A=b^(2)`

substitute

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

step 4

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

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

Simplify

Divide by 64 both numerator and denominator

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