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QuestionFind the actual area of a family room measuring 5 cm×4 cm5 \mathrm{~cm} \times 4 \mathrm{~cm} on a scale of 1 cm=1.5 m1 \mathrm{~cm}=1.5 \mathrm{~m}.

Studdy Solution

STEP 1

Assumptions1. The scale of the floor plan is1 cm =1.5 m. The dimensions of the family room in the plan are5 cm by4 cm3. We need to find the actual area of the family room in square meters

STEP 2

First, we need to convert the dimensions of the family room from the scale to actual size. We can do this by multiplying the dimensions in the plan by the scale factor.
Actual length=Plan lengthtimesScale factorActual\, length = Plan\, length \\times Scale\, factorActual width=Plan widthtimesScale factorActual\, width = Plan\, width \\times Scale\, factor

STEP 3

Now, plug in the given values for the plan length, plan width, and scale factor to calculate the actual length and width.
Actual length=5 cmtimes1.5 m/cmActual\, length =5\, cm \\times1.5\, m/cmActual width= cmtimes1.5 m/cmActual\, width =\, cm \\times1.5\, m/cm

STEP 4

Calculate the actual length and width.
Actual length= cmtimes1. m/cm=7. mActual\, length =\, cm \\times1.\, m/cm =7.\, mActual width=4 cmtimes1. m/cm=6 mActual\, width =4\, cm \\times1.\, m/cm =6\, m

STEP 5

Now that we have the actual length and width, we can find the actual area of the family room. The area of a rectangle is given by the formulaArea=LengthtimesWidthArea = Length \\times Width

STEP 6

Plug in the values for the actual length and width to calculate the area.
Area=.5 mtimes6 mArea =.5\, m \\times6\, m

STEP 7

Calculate the area of the family room.
Area=7.5 mtimes6 m=45 m2Area =7.5\, m \\times6\, m =45\, m^2The actual area of the family room is45 square meters.

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