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Question Number 74293 by Mr. K last updated on 21/Nov/19

Commented by Mr. K last updated on 21/Nov/19

$A B C D i d a q u a d r i l a t e r a l, c o s θ = \frac{\sqrt{7}}{4} .$ $A E = 1, B E = 4, C E = 3 a n d D E = 2 .$ $F i n d t h e a r e a o f t h e q u a d r i l a t e r a l .$
Commented by ~blr237~ last updated on 21/Nov/19

$l e t n a m e d i t S$ $S = A r e a (E A D) + A r e a (E D C) + A r e a (E C B) + A r e a (E B A)$ $A r e a (E A D) = \frac{1}{2} E A \times E D \times ∣ s i n (m e s A E D) ∣=∣ s i n θ ∣$ $c a u s e m e s A E D = θ$ $A r e a (E D C) = \frac{1}{2} E D \times E C \times ∣ s i n (m e s D E C) ∣= 3 ∣ s i n θ ∣$ $c a u s e m e s D E C = π - θ$ $A r e a (E C B) = \frac{1}{2} E C \times E B \times ∣ s i n θ ∣= 6 ∣ s i n θ ∣$ $A r e a (E B A) = \frac{1}{2} E B \times E A \times ∣ s i n (π - θ) ∣= 2 ∣ s i n θ ∣$ $S o S = 12 ∣ s i n θ ∣$ $S^{2} = 144 (1 - {c o s}^{2} θ) = 144 (1 - \frac{7}{16}) = \frac{144 \times 9}{16}$ $f i n a l l y S = \frac{12 \times 3}{4} = 9$ $c h e c k i f t h e r e i s n o t a n y m i s t a k e$
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