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The area of a square floor on a scale drawing is 81 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? 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.

Respuesta :

MissPhiladelphia
The area of a square floor on a scale drawing is 81 square centimeters, and the scale drawing is 1 centimeter:2 ft. 
so the original area is
A = 81 sq cm ( 2 ft / 1 cm)^2a = 324 sq ft
so the ratio of the ratio the area in the drawing to the actual area  is:
r = 81 sq cm / 324 sq ftr = 1 sq cm / 4 sq ft1 sq cm : 4 sq ft

Step-by-step explanation:

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

1 cm

3 ft

 

1 centimeter in the drawing equals 3 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 81 square centimeters, so the side length must be 9 cm.

Find the side length of the actual floor represented by 9 cm in the scale model.

1 cm × 9

3 ft × 9

 =  

9 cm

27 ft

 

The side length of the actual floor is 27 ft.

Since the area of a square is the side length squared, the area of the actual floor is 729 square feet.

The ratio of the area in the drawing to the actual area is 81 square centimeters:729 square feet.

Simplify the ratio.

The ratio of the area in the drawing to the actual area is 1 square centimeter:9 square feet.