Consider quadrilateral ABCD same as in Q 1378 with same conditions/restrictions (Pl refer the Question again). • What could be possible minimum and maximum area of the quadrilateral? •When qusdrilateral has minimum area what is the value/s of m∠A? Similarly what is value/s of m∠A in case of maximum area?


Question and Answers Forum

All Questions Topic List
Geometry Questions
Previous in All Question Next in All Question
Previous in Geometry Next in Geometry
Question Number 1395 by Rasheed Soomro last updated on 28/Jul/15

$C o n s i d e r quadrilateral ABCD s a m e a s i n Q 1378 w i t h$ $s a m e c o n d i t i o n s / r e s t r i c t i o n s (P l r e f e r t h e Q u e s t i o n a g a i n) .$ $∙ W h a t c o u l d b e p o s s i b l e minimum a n d maximum area$ $o f t h e q u a d r i l a t e r a l ?$ $∙ W h e n q u s d r i l a t e r a l h a s minimum area w h a t i s t h e v a l u e / s$ $o f m ∠ A ? S i m i l a r l y w h a t i s v a l u e / s o f m ∠ A i n c a s e o f$ $maximum area ?$
Commented by prakash jain last updated on 28/Jul/15

$minimum area \to 0$ $maximum area \to {(\frac{a + b + c + d}{4})}^{2}$ $m ∠ A for \max area \to \frac{π}{2}$
Commented by Rasheed Soomro last updated on 29/Jul/15

$I n o r d e r t o l e a r n I p u t m y q u e s t i o n s (r a i s e d i n m y m i n d)$ $b e f o r e y o u . I w a n t t o b e s a t i s f i e d, s o Please reply .$ $m a x i m u m a r e a \to {(\frac{a + b + c + d}{4})}^{2}$ $∙ Y o u h a v e u s e d s y m b o l^{'} \to^{'} i n a b o v e . D o e s t h i s m e a n^{'} t e n d s t o^{'} ?$ $∙ C o u l d w e r e p l a c e i t w i t h^{'} =^{'} e q u a l l y ?$ $∙ D o e s t h e a b o v e e x p r e s s i o n c a n b e u s e d a s a f o r m u l a f o r$ $t h e a r e a a quadrilateral having one angle of \frac{π}{2} rad . I f y e s$ $t h e n i t s h o u l d b e u s e d f o r a r e a o f r e c t a n g l e o f x by y .$ $B u t a b o v e f o r m u l a g i v e s t h e a r e a (\frac{x + y}{2}) i n s t e a d o f x y!$ $I n o t h e r w o r d s :$ $B e i n g q u a d r i l a t e r a l m a x i m u m a r e a o f p a r a l l e l o g r a m i s$ $a r e a o f r e c t a n g l e . I f t h e d i m e n s i o n s o f ∥ g r a m a r e$ $x a n d y t h e n m a x i m u m a r e a s h o u l d b e x y . B u t t h e a b o v e$ $f o r m u l a g i v e s t h e r e s u l t \frac{x + y}{2}!$
Commented by Rasheed Soomro last updated on 29/Jul/15

$I t h i n k a s a r e a \to 0, m ∠ A \to 0 o r π$
Commented by prakash jain last updated on 29/Jul/15

$You can have area \to 0 with two opposite$ $side a and c, a \neq b near 0 .$
Commented by Rasheed Ahmad last updated on 31/Jul/15

$M a x i m u m a r e a o f p a r l l e l o g r a m$ $w i t h d i m e n s i o n s x a n d y i s t h e$ $a r e a o f r e c t a n g e w i t h s a m e$ $d i m e n s i o n s t h a t i s x y i f I a m r i g h t .$ $B u t y o u r f o r m u l a {(\frac{a + b + c + d}{4})}^{2}$ $g i v e s {(\frac{x + y}{2})}^{2} . P l e a s e e x p l a i n$ $a s I w a n t t o l e a r n f r o m y o u .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum