The area of a square floor on a scale drawing is 64 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? I have been trying to answer this question forever I missed the dead line my assignment was trying to answer this question can you please help thanks get back to me as soon as you can.
Step 1:
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.
Step 2:
Find the side length of the floor in the scale drawing.
The area of the square in the drawing is 64 square centimeters, so the side length must be 8 cm.
Step 3:
Find the side length of the actual floor represented by 8 cm in the scale model.
1 cm × 8
2 ft × 8
=
8 cm
16 ft
The side length of the actual floor is 16 ft.
Step 4:
Since the area of a square is the side length squared, the area of the actual floor is 256 square feet.
Step 5:
The ratio of the area in the drawing to the actual area is 64 square centimeters:256 square feet.
Simplify the ratio.
The ratio of the area in the drawing to the actual area is 1 square centimeter:4 square feet.
To find the area of the actual floor, we need to convert the measurements from the scale drawing to the actual measurements.
Given that the scale is 1 centimeter:2 ft, we can determine that 1 cm on the scale drawing represents 2 ft in reality.
So, to convert the area from square centimeters to square feet, we need to square the conversion factor (1 cm = 2 ft) and multiply it by the area of the scale drawing (64 square centimeters).
First, convert 1 cm to ft:
1 cm * (1 ft / 30.48 cm) = 0.0328 ft
Now, we square the conversion factor:
(0.0328 ft)^2 = 0.00108 ft^2
Finally, we calculate the area of the actual floor:
Area of actual floor = Area of scale drawing * Conversion factor
= 64 square centimeters * 0.00108 ft^2
≈ 0.06912 ft^2
Therefore, the area of the actual floor is approximately 0.06912 square feet.
To find the ratio of the area in the drawing to the actual area, we divide the area of the scale drawing by the area of the actual floor.
Ratio = Area of scale drawing / Area of actual floor
= 64 square centimeters / 0.06912 ft^2
To simplify the ratio, we need to convert square centimeters to square feet:
1 square centimeter * (1 ft^2 / 929.03 square centimeters) = 0.001076 ft^2
Now, we can calculate the ratio:
Ratio = (64 square centimeters * 0.001076 ft^2) / 0.06912 ft^2
Simplifying the ratio yields:
Ratio ≈ 0.9723
Therefore, the ratio of the area in the drawing to the actual area is approximately 0.9723.
To find the area of the actual floor, we need to convert the scale from centimeters to feet.
Given that the scale is 1 centimeter:2 ft, we can determine that 1 square centimeter in the scale drawing represents (2 ft)*(2 ft) = 4 square feet in the actual floor.
Since the area of the square floor in the scale drawing is 64 square centimeters, we can multiply it by the conversion factor (4 sq ft/sq cm) to get the actual area of the floor:
64 sq cm * 4 sq ft/sq cm = 256 sq ft
Therefore, the area of the actual floor is 256 square feet.
To find the ratio of the area in the drawing to the actual area, we can express it as a fraction. The area in the drawing is 64 square centimeters and the actual area is 256 square feet.
The ratio of the area in the drawing to the actual area can be calculated as:
(64 sq cm) / (256 sq ft)
To make the units consistent, we need to convert square centimeters to square feet. Since there are 929.03 square centimeters in 1 square foot, we can divide the numerator by 929.03:
(64 sq cm) / (929.03 sq cm/sq ft) ≈ 0.07 sq ft
Therefore, the ratio of the area in the drawing to the actual area is approximately 0.07.
The square root of 64 = 8 cm
1 cm = 2 ft
8 cm = 16 ft
A = 16^2 sq. ft