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Video: Conversion of Units of Area

Ed Burdette

Soccer fields vary in size. A large soccer field is 115 m long and 85.0 m wide. What is its area in square feet? (Assume that 1 m = 3.281 ft.)

02:17

Video Transcript

Soccer fields vary in size. A large soccer field is 115 meters long and 85.0 meters wide. What is its area in square feet? Assume that one meter equals 3.281 feet.

Letโ€™s call the area in square feet capital ace of ๐‘“. We can begin by solving for the area of the field in meters squared in the original dimensions given. Weโ€™re told the field is 115 meters long. Weโ€™ll call that capital ๐ฟ, and that the field is 85.0 meters wide. Weโ€™ll call that capital ๐‘Š for width. The area of the field in meters, ace of ๐‘š, is equal to length times width, ๐ฟ times ๐‘Š.

When we insert the values for these terms and multiply them together, we find an area in square meters of 9775 meters squared. We now want to take this area and convert it to units from meters squared to feet squared, and weโ€™re told that one meter equals 3.281 feet which weโ€™ll assume is an exact relationship.

This means that if we multiply 9775 meters squared by 3.281 feet per meter and then square our conversion fraction, then notice how the meters squared terms cancel out leaving us with an equivalent area in feet squared, namely ๐ด sub ๐‘“, the value weโ€™re solving for. ๐ด sub ๐‘“ is equal to 9775 times 3.281 feet quantity squared.

When we multiply those values together, we find an area of 1.05 times 10 to the fifth feet squared. This is the area of the soccer field in square feet.