The bases of a trapezoid measure 1/4 and 3/8 inches, and the height is 1 inch. what is the area of the trapezoid?
a.1/6 in^2
b.5/16 in^2
c.4/5 in^2
d. 2 1/8in^2

The answer is:  [B]:  " 5/16  in² " . 

Explanation:

Formula for Area, "A", of a trapezoid:
 
    A = (½) * (b₁ + b₂) * h ;

or, write as:  A = (b₁ + b₂)*h / 2 ;

in which: A = Area of the trapezoid ;
    b₁ = length of one of the bases of the trapezoid (choose any of the two);
    b₂ = length of the other base of the trapezoid (the remaining one);
    h = height of the trapezoid ;

Given:

b₁ = ¼ in ;
b₂ = ⅜ in ;
h  = 1 in ;

Find the Area:

Plug in these values given into the formula;
    and solve for the "Area" of the trapezoid:

        →    A = (½) * (b₁ + b₂) * h 

        →    A = (½) * (¼ in  +  ⅜ in) * (1 in) ;

 →  (Note:  Let us simplify:  "(¼ in  +  ⅜ in)" ;
              ¼ + ⅜ =  ??
           ¼ = ?/ 8 ?? ;  →  8÷4 =2 ;  2*4 = 8 ;

       So, 1/4 = (1*2) / (4*2) = 2/8  ;

So;  (¼ in  +  ⅜ in) = 2/8 in  + ⅜ in = (2+3)/8 in = ⅝ in.

So rewrite:

         →    A = (½) * (¼ in  +  ⅜ in) * (1 in) ;
 
substituting: "( ⅝ in)" for "(¼ in  +  ⅜ in)" ;  AS FOLLOWS:

        →    A = (½) * (⅝ in) * (1 in) ;

        →    A = [ (½) * (⅝) ]  in²  ; 

        →    A = [(1*5) / (2*8)] in²

        →    A =  5/16   in² ; or, write as:  0.3125 in² ;

       →  Area =  5/16 in²  corresponds to: 
                                    "Answer choice:  [B]" .
  

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