Math Question and Answers


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 176318 by Matica last updated on 16/Sep/22

Commented by Rasheed.Sindhi last updated on 16/Sep/22

$f i n d a r e a o f q u a d r i l a t e r a l ABCD$
Commented by mr W last updated on 16/Sep/22

$A = \frac{\tan 45 °}{4} \times (8^{2} + 10^{2} - 2^{2} - 6^{2}) = 31$
Commented by Matica last updated on 16/Sep/22

$p l e a s e s a y m o r e d e t a i l$
	Answered by mr W last updated on 16/Sep/22

	Commented by mr W last updated on 16/Sep/22

	$A_{1} = \frac{e f \sin θ}{2}$ $A_{2} = \frac{f g \sin θ}{2}$ $A_{3} = \frac{g h \sin θ}{2}$ $A_{4} = \frac{h e \sin θ}{2}$ $A = A_{1} + A_{2} + A_{3} + A_{4}$ $a^{2} = e^{2} + f^{2} - 2 e f \cos θ$ $\Rightarrow a^{2} = e^{2} + f^{2} - \frac{4 A_{1}}{\tan θ} . . . (i)$ $b^{2} = f^{2} + g^{2} + 2 f g \cos θ$ $\Rightarrow b^{2} = f^{2} + g^{2} + \frac{4 A_{2}}{\tan θ} . . . (i i)$ $c^{2} = g^{2} + h^{2} - 2 g h \cos θ$ $\Rightarrow c^{2} = g^{2} + h^{2} - \frac{4 A_{3}}{\tan θ} . . . (i i i)$ $d^{2} = h^{2} + e^{2} + 2 h e \cos θ$ $\Rightarrow d^{2} = h^{2} + e^{2} + \frac{4 A_{4}}{\tan θ} . . . (i v)$ $(i i) + (i v) - (i) - (i i i) :$ $- a^{2} - c^{2} + b^{2} + d^{2} = \frac{4 (A_{1} + A_{2} + A_{3} + A_{4})}{\tan θ}$ $\Rightarrow A = \frac{∣ \tan θ ∣∣ (a^{2} + c^{2} - b^{2} - d^{2}) ∣}{4}$ $(θ \neq 90 °)$
	Commented by Matica last updated on 16/Sep/22

	$T h a n k y o u$
	Commented by Tawa11 last updated on 18/Sep/22

	$Great sir$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum