Math Question and Answers


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 160839 by amin96 last updated on 07/Dec/21

Commented by amin96 last updated on 07/Dec/21

$yellow area = ?$
	Answered by mr W last updated on 08/Dec/21

	Commented by mr W last updated on 08/Dec/21

	$M e t h o d I (n o t s o s m a r t o n e)$ $\frac{A B}{\sin (α + 60)} = \frac{2}{\sin (α + 30)}$ $A B = \frac{2 \sin (α + 60)}{\sin (α + 30)}$ $\frac{D B}{\sin α} = \frac{2}{\sin (α + 30)}$ $D B = \frac{2 \sin α}{\sin (α + 30)}$ $S_{1} = \frac{1}{2} \times 2 \times \frac{2 \sin (α + 60)}{\sin (α + 30)} \times \sin 30 = \frac{\sin (α + 60)}{\sin (α + 30)}$ $S_{2} = \frac{1}{2} \times 2 \times \frac{2 \sin α}{\sin (α + 30)} \times \sin 30 = \frac{\sin α}{\sin (α + 30)}$ $S_{y e l l o w} = \frac{\sin (α + 60) + \sin α}{\sin (α + 30)}$ $= \frac{\sin (α + 30 + 30) + \sin (α + 30 - 30)}{\sin (α + 30)}$ $= \frac{2 \sin (α + 30) \cos 30}{\sin (α + 30)}$ $= 2 \cos 30 = \sqrt{3}$
	Commented by Tawa11 last updated on 08/Dec/21

	$Great sir .$
	Answered by mr W last updated on 08/Dec/21

	Commented by mr W last updated on 08/Dec/21

	$M e t h o d I I$ $m a k e Δ D E A = Δ C D B a s s h o w n$ $y e l l o w a r e a = a r e a o f t r a p a z o i d A B D E$ $D E / / B A$ $B D = A E$ $B E = A D = 2$ $a r e a o f t r a p a z o i d = \frac{A D \times B E \times \sin 60}{2}$ $= 2 \sin 60 = \sqrt{3}$
	Commented by Ari last updated on 09/Dec/21
	Mr.Why area of trapezoid is (ADBEsin60)/2.This fomule is true for each trapezoid?
	Commented by mr W last updated on 09/Dec/21

	${i t}^{'} s t r u e f o r a n y c o n v e x q u a d r i l a t e r a l!$ $A = \frac{d i a g o n a l 1 \times d i a g o n a l 2 \times \sin θ}{2}$
	Commented by Ari last updated on 09/Dec/21
	ok,thanks!
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum