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Diketahui kubus ABCDEFGH dengan panjang rusuk. Jarak titik B ke bidang AFC sama dengan ...

Diketahui kubus ABCDEFGH dengan panjang rusukbegin mathsize 14px style equals 6 space cm end style. Jarak titik B ke bidang AFC sama dengan ... 

Jawaban:

Perhatikan gambar kubus tersebut berikut ini 


 


Jarak titik B ke bidang begin mathsize 14px style AFC end style sama dengan panjang begin mathsize 14px style BP end style. Perhatikan pada segitiga begin mathsize 14px style BOF end style siku-siku di B 


  

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row BD equals cell square root of BA squared plus AD squared end root end cell row blank equals cell square root of 6 squared plus 6 squared end root end cell row blank equals cell square root of 36 plus 36 end root end cell row blank equals cell square root of 72 end cell row blank equals cell 6 square root of 2 space cm end cell row blank blank blank row BO equals cell 1 half cross times BD end cell row blank equals cell 1 half cross times 6 square root of 2 end cell row blank equals cell 3 square root of 2 end cell row blank blank blank row OF equals cell square root of OB squared plus BF squared end root end cell row blank equals cell square root of open parentheses 3 square root of 2 close parentheses squared plus 6 squared end root end cell row blank equals cell square root of 18 plus 36 end root end cell row blank equals cell square root of 54 end cell row blank equals cell 3 square root of 6 space cm end cell end table end style  

Dengan menggunakan rumus kesamaan luas pada segitiga begin mathsize 14px style BOF end style, diperoleh 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 1 half cross times OB cross times BF end cell equals cell 1 half cross times OF cross times BP end cell row cell 1 half cross times 3 square root of 2 cross times 6 end cell equals cell 1 half cross times 3 square root of 6 cross times BP end cell row cell 18 square root of 2 end cell equals cell 3 square root of 6 BP end cell row BP equals cell fraction numerator 18 square root of 2 over denominator 3 square root of 6 end fraction end cell row BP equals cell fraction numerator 6 over denominator square root of 3 end fraction end cell row BP equals cell 2 square root of 3 space cm end cell end table end style 

Jadi Jarak titik B ke bidang begin mathsize 14px style AFC end style adalah begin mathsize 14px style 2 square root of 3 space cm end style

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