QuestionFind the area in square inches of a scale drawing of a classroom floor measuring 24 ft by 30 ft, with a length of 4 in.

Studdy Solution

STEP 1

Assumptions1. The length of the classroom floor is24 feet. The width of the classroom floor is30 feet3. The scale drawing of the floor has a length of4 inches4. The scale is the same in both the length and width directions (since it's a rectangular floor)

STEP 2

First, we need to find the scale of the drawing. We can do this by dividing the length of the drawing by the length of the actual floor.
$Scale = \frac{Length\, of\, drawing}{Length\, of\, actual\, floor}$

STEP 3

Now, plug in the given values for the length of the drawing and the length of the actual floor to calculate the scale.
$Scale = \frac{\, inches}{24\, feet}$

STEP 4

Since the units are different, we need to convert feet to inches. We know that1 foot equals12 inches.
$24\, feet =24 \times12\, inches$

STEP 5

Calculate the length in inches.
$24\, feet =24 \times12\, inches =288\, inches$

STEP 6

Now, substitute the converted length into the scale formula.
$Scale = \frac{4\, inches}{288\, inches}$

STEP 7

Calculate the scale.
$Scale = \frac{4\, inches}{288\, inches} =0.0139\, inches/foot$

STEP 8

Now that we have the scale, we can find the width of the drawing by multiplying the actual width by the scale.
$Width\, of\, drawing = Actual\, width \times Scale$

STEP 9

Plug in the values for the actual width and the scale to calculate the width of the drawing.
$Width\, of\, drawing =30\, feet \times.0139\, inches/foot$

STEP 10

Calculate the width of the drawing.
$Width\, of\, drawing =30\, feet \times0.0139\, inches/foot =0.417\, inches$

STEP 11

Now that we have the length and width of the drawing, we can find the area of the drawing by multiplying the length by the width.
$Area\, of\, drawing = Length\, of\, drawing \times Width\, of\, drawing$

STEP 12

Plug in the values for the length and width of the drawing to calculate the area of the drawing.
$Area\, of\, drawing =4\, inches \times0.417\, inches$

STEP 13

Calculate the area of the drawing.
$Area\, of\, drawing =\, inches \times0.417\, inches =.668\, square\, inches$ The area of the floor in the scale drawing is.668 square inches.

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