The area of trapezoid trap is 100 m squared

tr= 10m and the height is 5m

find the length of pa

 30 m ; (or, write as: "30 meters") .

Explanation:


Area of a trapezoid, "A" = (1/2) ( b₁ + b₂) h ;

or, write as:  A = ( b₁ + b₂) h  / 2 ;

in which:  A = area;
              b₁ = length of "base 1" (choose either one of the 2 (two bases);
              b₂ = length of "base 2" (use the base that is remaining);
              h = height of trapezoid;

From the information given: 

A = 100 m² ; 
h = 5 m
b₁ = 10 m
b₂ =  x 

Find "x", which is:  "b₂" ;

      A = ( b₁ + b₂) h  / 2  ;

Plug in our known values; and plug in "x" for "b₂" ; and solve for "x" ;

  100 m² = [(10m + x) (5m)] / 2  ; Solve for "x" ;

          (10m + x) (5m) = (2)* (100m²) ;

             (5m) (10m + x) = 200 m² ;

Note:  The distributive property of multiplication:

    a(b+c) = ab + ac ;
 
    a(b−c) = ab − ac ;


  We have:  (5m) (10m + x) = 200 m²  ;

So:    (5m) (10m + x) =  (5m*10m) + (5m * x) ;
                           
                               =  50m² + (5m)x  ;

     →  50m² + (5m)x = 200m²  ; 

Divide the ENTIRE equation by "5m" ;

     → { 50m² + (5m)x } / 5m = (200m² / 5m) ;

     →  10m + x   = 40m ; 

Now, subtract "10m" from EACH side of the equation; to isolate "x" on one side of the equation; and to solve for "x" ;

     →  10m + x  − 10m  =  40m − 10m ;

to get:

                →    x  =  30 m  ; which is our answer.

 30 m ; (or, write as: "30 meters") .