Trevor makes a scale drawing of a dog house that he has building. The skill he uses is 1 inch colon 4/10 feet. What is the actual area of the floor of the dog house if they dimensions on the scale drawing or 8 inches by 10 inches?
8*(4/10) ft * 10*(4/10) ft = 12.8 ft^2
To find the actual area of the floor of the dog house, we need to convert the dimensions from the scale drawing to actual dimensions using the given scale.
First, let's convert the dimensions on the scale drawing to feet:
Length on scale drawing = 8 inches
Width on scale drawing = 10 inches
Using the scale of 1 inch : 4/10 feet, we can set up the following ratio:
1 inch / 8 inches = 4/10 feet / X
Now, we can solve for X (the actual length on the floor) by cross-multiplying:
1 inch * X = 8 inches * (4/10 feet)
Cancel out the units of inches:
X = (8 inches * 4 feet) / (10 inches)
Simplifying the expression:
X = 32/10 feet
X = 3.2 feet
Similarly, we can find the actual width on the floor:
1 inch / 10 inches = 4/10 feet / Y
Cross-multiplying:
1 inch * Y = 10 inches * (4/10 feet)
Cancel out the units of inches:
Y = (10 inches * 4 feet) / (10 inches)
Simplifying the expression:
Y = 4 feet
Now that we have the actual dimensions of the floor (length = 3.2 feet, width = 4 feet), we can calculate the actual area of the floor by multiplying these two dimensions:
Actual Area = Length * Width
Actual Area = 3.2 feet * 4 feet
Actual Area = 12.8 square feet
Therefore, the actual area of the floor of the dog house is 12.8 square feet.