The rectangular floor of a classroom is $38$ feet in length and $32$ feet in width. A scale drawing of the floor has a length of $19$ inches. What is the area, in square inches, of the floor in the scale drawing? $\newline$ Answer: $\square$ in. $^{2}$

View step-by-step help

Home

Math Problems

Grade 6

Area of quadrilaterals and triangles: word problems

Full solution

Q. The rectangular floor of a classroom is

38

feet in length and

32

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

19

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

\newline

Answer:

\square

in.

^{2}

Calculate Scale Factor: First, we need to determine the scale factor between the actual floor and the scale drawing. We do this by comparing the length of the actual floor to the length of the scale drawing. $\newline$ Scale factor $= \frac{\text{Length of scale drawing}}{\text{Length of actual floor}}$ $\newline$ Scale factor $= \frac{19 \text{ inches}}{38 \text{ feet}}$ $\newline$ Since there are $12$ inches in a foot, we need to convert $38$ feet into inches before we can find the scale factor. $\newline$ $38$ feet $= 38 \times 12$ inches $\newline$ $38$ feet $= 456$ inches $\newline$ Scale factor $= \frac{19 \text{ inches}}{456 \text{ inches}}$
Find Scale Drawing Width: Now we can calculate the scale factor. $\newline$ Scale factor = $\frac{19}{456}$ $\newline$ This can be simplified by dividing both the numerator and the denominator by $19$ . $\newline$ Scale factor = $\frac{1}{24}$
Calculate Area: Next, we need to find the width of the scale drawing using the scale factor. We know the actual width of the floor is $32$ feet, which we need to convert to inches and then apply the scale factor. $\newline$ Width of actual floor in inches = $32$ feet $* 12$ inches/foot $\newline$ Width of actual floor in inches = $384$ inches $\newline$ Width of scale drawing = Width of actual floor in inches $*$ Scale factor $\newline$ Width of scale drawing = $384$ inches $*(1 / 24)$
Calculate Area: Next, we need to find the width of the scale drawing using the scale factor. We know the actual width of the floor is $32$ feet, which we need to convert to inches and then apply the scale factor. $\newline$ Width of actual floor in inches = $32$ feet $* 12$ inches/foot $\newline$ Width of actual floor in inches = $384$ inches $\newline$ Width of scale drawing = Width of actual floor in inches $*$ Scale factor $\newline$ Width of scale drawing = $384$ inches $*(1 / 24)$ Now we calculate the width of the scale drawing. $\newline$ Width of scale drawing = $384$ inches $*(1 / 24)$ $\newline$ Width of scale drawing = $16$ inches
Calculate Area: Next, we need to find the width of the scale drawing using the scale factor. We know the actual width of the floor is $32$ feet, which we need to convert to inches and then apply the scale factor. $\newline$ Width of actual floor in inches = $32$ feet $*$ $12$ inches/foot $\newline$ Width of actual floor in inches = $384$ inches $\newline$ Width of scale drawing = Width of actual floor in inches $*$ Scale factor $\newline$ Width of scale drawing = $384$ inches $*$ $(1 / 24)$ Now we calculate the width of the scale drawing. $\newline$ Width of scale drawing = $384$ inches $*$ $(1 / 24)$ $\newline$ Width of scale drawing = $32$ $2$ inchesWe have the length and the width of the scale drawing, so we can now calculate the area of the scale drawing. $\newline$ Area of scale drawing = Length of scale drawing $*$ Width of scale drawing $\newline$ Area of scale drawing = $32$ $4$ inches $*$ $32$ $2$ inches
Calculate Area: Next, we need to find the width of the scale drawing using the scale factor. We know the actual width of the floor is $32$ feet, which we need to convert to inches and then apply the scale factor. $\newline$ Width of actual floor in inches = $32$ feet $*$ $12$ inches/foot $\newline$ Width of actual floor in inches = $384$ inches $\newline$ Width of scale drawing = Width of actual floor in inches $*$ Scale factor $\newline$ Width of scale drawing = $384$ inches $*$ $(1 / 24)$ Now we calculate the width of the scale drawing. $\newline$ Width of scale drawing = $384$ inches $*$ $(1 / 24)$ $\newline$ Width of scale drawing = $32$ $2$ inchesWe have the length and the width of the scale drawing, so we can now calculate the area of the scale drawing. $\newline$ Area of scale drawing = Length of scale drawing $*$ Width of scale drawing $\newline$ Area of scale drawing = $32$ $4$ inches $*$ $32$ $2$ inchesFinally, we calculate the area of the scale drawing. $\newline$ Area of scale drawing = $32$ $4$ $*$ $32$ $2$ $\newline$ Area of scale drawing = $*$ $0$ square inches