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The rectangular floor of a classroom is 40 feet in length and 20 feet in width. A scale drawing of the floor has a length of 20 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer: in.
^(2)

The rectangular floor of a classroom is $40$ feet in length and $20$ feet in width. A scale drawing of the floor has a length of $20$ inches. What is the area, in square inches, of the floor in the scale drawing? $\newline$ Answer: $\square$ in. $^{2}$

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Area of quadrilaterals and triangles: word problems

Full solution

Q. The rectangular floor of a classroom is

40

feet in length and

20

feet in width. A scale drawing of the floor has a length of

20

inches. What is the area, in square inches, of the floor in the scale drawing?

\newline

Answer:

\square

in.

^{2}

Convert to inches: Convert the actual length of the classroom to inches. $\newline$ Since there are $12$ inches in a foot, we multiply the length in feet by $12$ to get the length in inches. $\newline$ $40$ feet $\times 12$ inches/foot $= 480$ inches
Determine scale factor: Determine the scale factor between the actual classroom and the scale drawing. The actual length is $480$ inches and the length of the scale drawing is $20$ inches. Scale factor $= \frac{\text{Length of scale drawing}}{\text{Actual length}}$ Scale factor $= \frac{20 \text{ inches}}{480 \text{ inches}}$ Scale factor $= \frac{1}{24}$
Convert width to inches: Convert the actual width of the classroom to inches. $\newline$ Since there are $12$ inches in a foot, we multiply the width in feet by $12$ to get the width in inches. $\newline$ $20$ feet $\times 12$ inches/foot $= 240$ inches
Calculate width: Calculate the width of the classroom in the scale drawing using the scale factor. $\newline$ Width of scale drawing = Actual width $\times$ Scale factor $\newline$ Width of scale drawing = $240$ inches $\times$ $(1/24)$ $\newline$ Width of scale drawing = $10$ inches
Calculate area: Calculate the area of the scale drawing. $\newline$ Area = Length of scale drawing $\times$ Width of scale drawing $\newline$ Area = $20$ inches $\times$ $10$ inches $\newline$ Area = $200$ square inches

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