If E is the midpoint of the segment BC, L 1 ∥ L 2 , A D = 4 c m , D E = 5 c m , E A = 7 c m , find the area of the quadrilateral ABCD.

Question

If E is the midpoint of the segment BC,       L    1    ∥      L    2   ,   A  D  =  4  c  m  ,     D  E  =  5  c  m     ,  E  A  =  7  c  m , find the area of the quadrilateral ABCD.

Alexis Fields · Accepted Answer

Step 1Draw a line parallel to AD and passing through E. Suppose that that line intersects L1 and L2 at       C    ′   and       B    ′  , respectively.The triangle AED has half the area of the parallellogram   A      B    ′        C    ′    D .The parallelogram   A      B    ′        C    ′    D has the same area as the trapezoid because the triangle   B  E      B    ′   and   C  E      C    ′   are equal (ALA).Therefore the triangle AED has half the area of the trapezoid ABCD too.

Nylah Hendrix · Accepted Answer

Step 1Call the perpendicular distance between the lines k. Then the area of   △  C  D  E is       1    2    C  D      k    2    =            C      D      k        4    . . The area of   △  A  E  B is       1    2    A  B      k    2    =            A      B      k        4    . . The area of the trapezoid ABCD is   k            C      D      +      A      B        2   .Comparing these areas shows that   △  A  D  E is half the area of the trapezoid.

If E is the midpoint of the segment BC, L 1 </msub> ∥

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