If E is the midpoint of the segment BC, L 1 ∥ L 2 ,...

Rapsinincke

Rapsinincke

Answered

2022-07-11

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.

Answer & Explanation

Alexis Fields

Alexis Fields

Expert

2022-07-12Added 14 answers

Step 1
Draw 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

Nylah Hendrix

Expert

2022-07-13Added 1 answers

Step 1
Call 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.

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