QuestionFind the area in square inches of a scale drawing of a classroom floor measuring 24 ft by 40 ft with a length of 6 in.

Studdy Solution

STEP 1

Assumptions1. The actual floor is rectangular with a length of24 feet and a width of40 feet. . The scale drawing is also rectangular with a length of6 inches.
3. The scale of the drawing is consistent for both length and width.
4. The area of the floor in the scale drawing is to be found in square inches.

STEP 2

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

STEP 3

Now, plug in the given values for the length of the scale drawing and the length of the actual floor to calculate the scale.
$Scale = \frac{6\, inches}{24\, feet}$

STEP 4

Since we are comparing inches to feet, we need to convert feet to inches. There are12 inches in a foot.
$Scale = \frac{6\, inches}{24 \times12\, inches}$

STEP 5

Calculate the scale.
$Scale = \frac{}{24 \times12} = \frac{1}{8}$

STEP 6

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

STEP 7

Plug in the values for the width of the actual floor and the scale to calculate the width of the scale drawing.
$Width\, of\, scale\, drawing =40\, feet \\times \frac{1}{}$

STEP 8

Convert the width from feet to inches.
$Width\, of\, scale\, drawing =40 \times12\, inches \\times \frac{1}{8}$

STEP 9

Calculate the width of the scale drawing.
$Width\, of\, scale\, drawing =40 \times12 \\times \frac{}{8} =60\, inches$

STEP 10

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

STEP 11

Plug in the values for the length and width of the scale drawing to calculate the area.
$Area\, of\, scale\, drawing =6\, inches \\times60\, inches$

STEP 12

Calculate the area of the scale drawing.
$Area\, of\, scale\, drawing =6 \\times60 =360\, square\, inches$ The area of the floor in the scale drawing is360 square inches.

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