The question is The area of a square floor on a scale drawing is 25 square centimeters, and the scale drawing is 1 centimeter:4 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?
Please I need a awsner
25cm^2 = 5x5 cm
so the floor is (5*4)^2 = 400ft^2
or, since area scales as the square of the scale,
(1:4)^2 = 1:16
25*16 = 400
25 square centemeters = 5x5 centemeters. The floor is (5 times 4) squared = 400square feet. Or.......... since area scales as the square of the scale, (1:4) squared = 1:16, and 25 times 16 = 400. Hope u have a great day UwU.
To find the area of the actual floor, we need to convert the scale from centimeters to feet.
Given:
Scale: 1 centimeter: 4 feet
Area on scale drawing: 25 square centimeters
Step 1: Convert the area on the scale drawing from square centimeters to square feet.
Since 1 square centimeter is equal to 0.00107639 square feet, we can calculate the area on the scale drawing in square feet:
Area on scale drawing = 25 square centimeters × 0.00107639 square feet/square centimeter
Area on scale drawing = 0.02690975 square feet
Step 2: Calculate the area of the actual floor.
The area on the scale drawing represents the area of the actual floor. So, the area of the actual floor is also 0.02690975 square feet.
Step 3: Find the ratio of the area in the drawing to the actual area.
To calculate the ratio, we need to divide the area on the scale drawing by the area of the actual floor:
Ratio = Area on scale drawing / Area of the actual floor
Ratio = 0.02690975 square feet / 0.02690975 square feet
Ratio = 1
Therefore, the area of the actual floor is 0.02690975 square feet, and the ratio of the area in the drawing to the actual area is 1:1.
To find the area of the actual floor, we can use the given scale of 1 centimeter:4 feet. Let's go step by step to solve this problem:
Step 1: Calculate the side length of the square on the scale drawing.
Since the area of the square on the scale drawing is given as 25 square centimeters, we can find the side length by taking the square root of the area:
Side length = √(Area) = √(25 cm²) = 5 cm
Step 2: Convert the side length from centimeters to feet.
According to the given scale, 1 centimeter on the scale drawing represents 4 feet in reality. Therefore, we can convert the side length from centimeters to feet by multiplying by the scale factor:
Side length in feet = 5 cm * (4 ft/1 cm) = 20 ft
Step 3: Calculate the area of the actual floor.
The area of a square is given by the formula: Area = side length². Apply this formula to find the area of the actual floor:
Area = (Side length in feet)² = (20 ft)² = 400 ft²
Therefore, the area of the actual floor is 400 square feet.
Step 4: Calculate the ratio of the area in the drawing to the actual area.
The ratio of the area in the drawing to the actual area can be found by dividing the area on the scale drawing by the area of the actual floor:
Ratio = (Area on drawing)/(Area of actual floor) = 25 cm² / 400 ft²
To compare these two different units, we need to convert centimeters to feet. Since 1 foot is equal to 30.48 centimeters, we can convert the area on the scale drawing to square feet:
25 cm² * (1 ft/30.48 cm)² = (0.8224 ft²) ≈ 0.82 ft²
Now we can calculate the ratio of the areas:
Ratio = (Area on drawing)/(Area of actual floor) = 0.82 ft² / 400 ft²
Therefore, the ratio of the area in the drawing to the actual area is approximately 0.002.