How many square inches are in 9 square yards? [ 1 yard = 3 feet ] [ 1 feet = 12 inches ]

Question

and how to get the answer

Answer 1

Use dimensional (or unit) analysis by setting up a "daisy chain" of conversion factors in the form of fractions that multiply out to give the required answer in square inches.

First need the conversions: 1 sq yd = 3 ft x 3 ft = 9 sq ft

1 sq ft = 12 in x 12 in = 144 sq in

9 sq yds/1 x 9 sq ft/1 sq yd x 144 sq in/1 sq ft = 11,664 sq in. Notice how the "sq yds" and "sq ft" unit cancel out, leaving the desired sq in. value. (Would be easier to see if I could use horizontal fraction bars).

Answer 2

Here's one way to think about it: using the definition of the area of a square, if you have a square with side length = 3 yards, then you have 9 yrd² since area of a square is side length squared and 3² = 9

In order to convert 9 yrd² to in² take your side length of 3 yards and convert to inches:

3 ft/yrd × 3 yards = 9ft

12 in/ft × 9 ft = 108 inches

So, if square your side length of 108 inches -- this will be equivilent to 9 yrd², given in in²

108² = 11,664 in² = 9 yrd²

Hope this helps,

Todd