Question

The area of a square floor on a scale drawing is 16 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?

Answer 1

Area of the actual floor = 144 ft²

Ratio = 1 cm² : 9 ft²

Explanation:

Area of the actual floor

The area of a square is equal to the square of its side length. Therefore, if the area of a square floor on a scale drawing is 16 cm², we can determine its side length by square rooting its area:

`\textsf{Side length}=√(16\;\sf cm^2)=4\;\sf cm`

Given that 1 cm on the scale drawing represents 3 ft in reality, the side length of the actual floor is:

`\sf 4\; cm * 3\; ft/cm = 12\;ft`

To find the area of the actual floor, we can square its side length:

`\sf (12\; ft)^2 = 144 \; ft^2`

Therefore, the area of the actual floor is:

`\Large\boxed{\boxed{\sf Area=144\; ft^2}}`

`\hrulefill`

Ratio of the areas

The ratio of the area in the drawing to the actual area is:

`\sf 16 \;cm^2 : 144\; ft^2`

Simplify by dividing both sides of the ratio by 16:

`\sf 1 \; cm^2 : 9 \; ft^2`

Therefore, the ratio of the area in the drawing to the actual area is:

`\Large\boxed{\boxed{\sf Ratio=1\;cm^2:9\; ft^2}}`

Answer 2

Area of actual floor = 144 cm²

Ratio of the area in the drawing to the actual area = 1:9.

Explanation:

Given:

• Area of square floor on scale drawing: 16 square centimeters
• Scale drawing scale: 1 centimeter:3 feet

To find:

• Area of actual floor.
• Ratio of the area in the drawing to the actual area.

Solution:

To find the area of the actual floor, we multiply the area of the square floor on the scale drawing by the square of the scale factor.

`\textsf{Area of actual floor = Area of scale drawing}* \textsf{ (Scale factor)}^2`

Area of actual floor = 16cm² × (3)²

Area of actual floor =16cm² × 9

Area of actual floor = 144 cm²

And

To find the ratio of the area in the drawing to the actual area, we simply divide the area of the scale drawing by the area of the actual floor.

`\sf \textsf{Ratio of area in drawing to actual area} = \frac{\textsf{Area of scale drawing }}{\textsf{ Area of actual floor}}`

`\sf \textsf{Ratio of area in drawing to actual area}=( 16cm^2 )/( 144cm^2)`

`\sf \textsf{Ratio of area in drawing to actual area }=( 1 )/( 9)`

Therefore, the area of the actual floor is 144 cm², and the ratio of the area in the drawing to the actual area is 1:9.