Question-161578

Question Number 161578 by Ari last updated on 19/Dec/21

Commented by blackmamba last updated on 20/Dec/21

\cos 75 ° = \frac{\frac{1}{2} a}{10} = \frac{a}{20}

\frac{1}{2} \sqrt{2} . \frac{1}{2} \sqrt{3} - \frac{1}{2} \sqrt{2} . \frac{1}{2} = \frac{a}{20}

\Rightarrow \sqrt{6} - \sqrt{2} = \frac{a}{5}

\Rightarrow a = 5 \sqrt{2} (\sqrt{3} - 1) c m

∴ S [B D H F] = a^{2} \sqrt{2} {c m}^{2}

= 50 \sqrt{2} (4 - 2 \sqrt{3}) {c m}^{2}

= 100 \sqrt{2} (2 - \sqrt{3}) {c m}^{2}

Answered by Rasheed.Sindhi last updated on 20/Dec/21

a^{2} = 10^{2} + 10^{2} - 2.10.10 . \cos 30

a = \sqrt{200 - 200 \cdot \frac{\sqrt{3}}{2}} = 10 \sqrt{2 - \sqrt{3}}

d = \sqrt{a^{2} + a^{2}} = a \sqrt{2} = 10 \sqrt{2 - \sqrt{3}} \cdot \sqrt{2}

S_{H D B F} = a d = (10 \sqrt{2 - \sqrt{3}}) (10 \sqrt{2 - \sqrt{3}} \cdot \sqrt{2})

= 100 (2 - \sqrt{3}) \sqrt{2} {cm}^{2}