Find the area of a square that is 1/2 yd on a side.

  "    yd²  " .

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The area of the square is:  "    yd²  " .

    or; write as:  " 0.25 yd² " . 
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Explanation:
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A "square", by definition, is a quadrilateral and a rectangle, with 4 (four) equal sides and 4 (four) equal angles.

The formula for the area of a square is:

                " A  =  s²  " ;  

          in which:  " A = area of the square" ;
 
        (in " square units ";  in our case, " square yards " ;  
                                                  or, write as:  " yd² " . 
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                           " s = side length = " 1/2 yd " ;  {given} .
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 To find the "Area, "A" ; of the square, which is what the question asks:  

→  We plug in the given / known values into the formula, & solve:

     →  " A  =  s²  "  ; 

     →    A = (1/2 yd)²  ; 

                =  (1/2)² * yd²  ;

                =  (1/2) * (1/2) * yd²  ; 

                = (1 * 1) / (2 * 2) * yd²  ;

                =  "  1/4 yd² " .
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 "   yd²  " .

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The area of the square is:  "    yd²  " .

    or; write as:  " 0.25 yd² " . 
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The answer is the third choice