Question-206737

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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