Question

The area of a square floor on a scale drawing is 36 square centimeters, and the scale drawing is 1 centimeter:2 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

Answer:

The actual area of the floor is 144 square feet. And the ratio in the drawing to the actual area is 1 square centimeter: 4 square feet

Step-by-step explanation:

Find the number of feet represented by 1 centimeter in the scale drawing.

1 cm/2 ft

1 centimeter in the drawing equals 2 feet on the actual floor.

Find the side length of the floor in the scale drawing.

The area of the square in the drawing is 36 square centimeters, so the side length must be 6 cm.

Find the side length of the actual floor represented by 6 cm in the scale model.

1 cm × 6/2 ft × 6 = 6 cm/12 ft

The side length of the actual floor is 12 ft.

Since the area of a square is the side length squared, the area of the actual floor is 144 square feet.

The ratio of the area in the drawing to the actual area is 36 square centimeters:144 square feet.

Simplify the ratio.

The ratio of the area in the drawing to the actual area is 1 square centimeter:4 square feet.

Hope it helps!

Answer 2

You can use the formula of area of square and then the ratio to find the answers.

The area of actual floor is 144 square feet.

The ratio of the area in the drawing to the actual area is 1 sq cm : 4 sq. ft

Given that:

• The area of square floor on drawing = 36 square centimetres
• Scale of drawing is 1 cm: 2 ft.

To find:

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

Formula for area of square with side length a  units:

$\text{A} = a \times a = a^2 \text{\: square units}$

Let the side length of the square floor be a units, then we have:

$\text{Area of floor in drawing }= a^2\\ 36 = a^2\\ a = \sqrt{36} \text{\: (positive root since length is non negative quantity)}\\ a = 6 \: \rm cm$

Since 1 cm in drawing is 2 feet in real world, thus we have:

$\text{Length of floor} = 6 \times 2 = 12 \: \rm feet$

Area of floor = square of length of floor

$\text{Area of floor} = 12^2 = 144 \: \rm feet^2$

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

$\dfrac{\text{area of floor in drawing}}{\text{area of floor}} = \dfrac{36 \: \rm cm^2}{144 \: \rm ft^2} = \dfrac{1 \: \rm cm^2}{4 \: \rm ft^2}$

Thus, the needed ratio is 1 sq cm : 4 sq. ft

Learn more about area of square and scaling here:

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