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A room has a length of 20' and a width of 10'. What is the area of this room in square meters?

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2 Answers

You are given that the length of the room is 20' (i.e., 20 feet) and its width is 10' (i.e., 10 feet). 

The area, A, of the room is found by multiplying the length, L, of the room by the width, W, of the room:

     A = L · W

     A = 20 ft · 10 ft

     A = 200 ft2 

Thus, the are of the room is 200 square feet.

 

Since we are asked to find the area of the room in square meters (i.e., m2), we need to convert 200 ft2 to m2:

           200 ft2    ·    (12 in)2    ·    (2.54 cm)2    ·      (1 m)         

                             _______         _________        _________

                               (1 ft)2              (1 in)2            (100 cm)2 

      =  200 ft2     ·     144 in2     ·      6.4516 cm2     ·         1 m2 

                             ________        ____________        ___________

                                 1 ft2                  1 in2                 10,000 cm2 

      =  18.580608 m2

      ≈  18.58 m2 

Thus, the area of the room is approximately 18.58 square meters.

This problem requires two steps:  1.  Converting from English to metric (the marking next to 10 and 20 means feet) 2.  Finding the area of a rectangle.  The steps can be taken in either order.  I am going to do them in the order that I listed.

1.  The exact conversion string would list as follows (In recent years, the inch has been redefined as 2.54 cm)

12 inch/1 ft X 2.54 cm/1 inch X 1 m/100 cm = .3048 m/ft

To convert feet to meters, we will multiply the number of feet by .3048 m/ft

20 ft X .3048 m/ft = 6.096 m

10 ft X .3048 m/ft = 3.048 m

2.  To find the area, multiply the length by the width

6.096 m * 3.048 m = 18.580608 m2 (approximately 18.6 m2)

 

You can solve the problem by finding the area in square feet and then converting, but you must remember to square the conversion factor when you convert to square meters.

 

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