1-Evaluer-Aire-A-B-C-D-2-En-deduire-Aire-A-B-C-D-Aire-ABCD-

Question Number 189233 by a.lgnaoui last updated on 13/Mar/23

1 ∙ E v a l u e r : A i r e (A^{'} B^{'} C^{'} D^{'})

2 ∙ E n d e d u i r e : \frac{A i r e (A^{'} B^{'} C^{'} D^{'})}{A i r e (A B C D)}

Commented by a.lgnaoui last updated on 13/Mar/23

[A^{'} B^{'} D] a l i g n e s

Commented by a.lgnaoui last updated on 13/Mar/23

Answered by HeferH last updated on 14/Mar/23

Commented by HeferH last updated on 14/Mar/23

{\begin{cases} 3 a = \frac{b}{\sqrt{3}} \\ a \sqrt{3} + b = 5 \sqrt{3} \end{cases}

∙ 3 a \sqrt{3} + a \sqrt{3} = 5 \sqrt{3}

a = \frac{5}{4} \Rightarrow b = \frac{15 \sqrt{3}}{4}

∙ a \times b = \frac{75 \sqrt{3}}{16}

∙ \frac{Area (A^{'} B^{'} C^{'} D^{'})}{Area (ABCD)} = \frac{75 \sqrt{3}}{16} \times \frac{1}{25 \sqrt{3}} = \frac{3}{16}

Commented by a.lgnaoui last updated on 14/Mar/23

e x a c t l y . t h a n k y o u