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Question Number 206737 by mr W last updated on 23/Apr/24

Commented by A5T last updated on 23/Apr/24

$I s t h a t s i g n i f i e d a n g l e 90 ° o r a n y ?$
Commented by mr W last updated on 23/Apr/24

$90 °$
Commented by A5T last updated on 23/Apr/24

$108 ?$
Commented by mr W last updated on 23/Apr/24

$r i g h t!$
	Answered by A5T last updated on 23/Apr/24

	Commented by A5T last updated on 23/Apr/24

	$\frac{D G}{A G} = \frac{10}{16} = \frac{5}{8}; D G = 5 x; A G = 8 x$ $\frac{C G}{B G} = \frac{5}{8}; C G = 5 y; B G = 8 y$ $25 x^{2} = 100 + 25 y^{2} \Rightarrow x^{2} - y^{2} = 4 \Rightarrow x = \sqrt{4 + y^{2}}$ $E C = 8 x - 12 - 5 y = 8 \sqrt{4 + y^{2}} - 5 y - 12$ $A C = 8 \sqrt{4 + y^{2}} - 5 y; B D = 8 y - 5 \sqrt{4 + y^{2}}$ $B F = 8 y - 5 \sqrt{4 + y^{2}} - 6$ $[A B D C] = \frac{A B \times B D + A C \times C D}{2} = 39 y$ $[B F A] + [D E C] = \frac{A B \times B F + E C \times D C}{2} = 39 y - 108$ $\Rightarrow [F A E D] = 39 y - (39 y - 108) = 108$
	Commented by mr W last updated on 23/Apr/24
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	Answered by mr W last updated on 23/Apr/24

	Commented by mr W last updated on 23/Apr/24

	$A_{1} = \frac{12 \times 10}{2} = 60$ $A_{2} = \frac{6 \times 16}{2} = 48$ $g r e e n a r e a = 60 + 48 = 108$
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