A scale drawing of an office space uses a scale of 1 in. : 6 yd. The scale drawing has an area of 6 square inches. What is the area of the actual office space?
Since the scale is 1 in. : 6 yd, this means that 1 inch on the scale drawing represents 6 yards in the actual office space.
The area of the scale drawing is given as 6 square inches. Since the lengths are in inches, we can assume that the area is in square inches.
Let's assume the length of the office space in inches is L inches. Then the length of the actual office space is 6 times the length of the scale drawing.
Since the area of a rectangle is given by length × width, we can write an equation for the area of the actual office space:
(area of actual office space) = (length of actual office space) × (width of actual office space)
Let's assume the width of the office space in inches is W inches. Then the width of the actual office space is 6 times the width of the scale drawing.
So, we have:
(area of actual office space) = (6L inches) × (6W inches)
Given that the area of the scale drawing is 6 square inches, we can substitute that information into the equation:
6 = (6L inches) × (6W inches)
Simplifying the equation, we have:
6 = 36LW inches squared
Dividing both sides of the equation by 36, we have:
6/36 = LW inches squared
1/6 = LW inches squared
This equation tells us that LW is equal to 1/6 square inches.
Since LW is equal to the area of the actual office space in square inches, the area of the actual office space is 1/6 square inches.