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Question Number 5441 by Rasheed Soomro last updated on 15/May/16

Commented by Rasheed Soomro last updated on 15/May/16

$(a) AB = a, BC = b, Area EFGH = ?$ $(b) Prove that if ABCD is a rectangle$ $then EFGH is a parallelogram .$ $(c) Prove that if ABCD is a square$ $then EFGH is also a square .$ $N o t e t h a t E, F, G, H a r e p o i n t s o n d i a g o n a l s$ $o b t a i n e d i n s u c h a w a y t h a t$ $AE = AB, BF = BC, CG = CD, DH = DA$
Commented by Rasheed Soomro last updated on 15/May/16

$^{∙} What if ABCD would be a parallelogram, a quadrilateral ?$ $^{∙} It is interesting to place some restrictions on$ $ABCD and to see an effect on EFGH! For example$ $ABCD may be non - convex, self intersecting, two$ $sides parallel etc .$
Commented by Yozzii last updated on 15/May/16

$I^{'} l l t r y i t s o o n . I^{'} v e b e e n b u s y .$
Commented by Yozzii last updated on 17/May/16

$A n a p p r o a c h b y u s e o f a n a l y t i c g e o m e t r y$ $p r o v e s (b) a n d (c) . (a) c a n b e f o u n d$ $u s i n g t h e f o r m u l a A = 0.5 p q s i n θ, w h e r e$ $p, q = l e n g t h o f d i a g o n a l s o f E F G H$ $a n d θ = a n g l e b e t w e e n t h e d i a g o n a l s$ $o f E F G H .$
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