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Pertanyaan

Perhatikan balok ABCD.EFGH berikut ini!

Tentukan panjang diagonal bidang, diagonal ruang, dan luas bidang diagonal pada balok ABCD.EFGH di atas!

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F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight p equals cell 16 space cm space space end cell row straight l equals cell 8 space cm space space end cell row straight t equals cell 12 space cm space end cell end table end style 

  • Diagonal bidang

begin mathsize 14px style AC equals BD equals EG equals FH space end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AC squared end cell equals cell AB squared plus BC squared end cell row blank equals cell 16 squared plus 8 squared end cell row blank equals cell 256 plus 64 end cell row blank equals 320 row AC equals cell plus-or-minus square root of 320 end cell end table end style 

karena panjang sisi, maka AC non negatif sehingga begin mathsize 14px style AC equals 8 square root of 5 blank cm end style 

Jadi, panjang diagonal bidang  begin mathsize 14px style bottom enclose bold AC bold equals bold BD bold equals bold EG bold equals bold FH bold equals bold 8 square root of bold 5 blank bold cm end enclose end style 

begin mathsize 14px style BG equals FC equals AH equals ED end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BG squared end cell equals cell BC squared plus CG squared end cell row blank equals cell 8 squared plus 12 squared end cell row blank equals cell 64 plus 144 end cell row blank equals 208 row BG equals cell plus-or-minus √ 208 end cell end table end style 

karena panjang sisi, maka BG non negatif sehingga begin mathsize 14px style BG equals 4 square root of 13 blank cm end style 

Jadi, panjang diagonal bidang begin mathsize 14px style bottom enclose bold BG bold equals bold FC bold equals bold AH bold equals bold ED bold equals bold 4 square root of bold 13 blank bold cm end enclose end style  

begin mathsize 14px style AF equals BE equals CH equals DG end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AF squared end cell equals cell AB squared plus FB squared end cell row blank equals cell 16 squared plus 12 squared end cell row blank equals cell 256 plus 144 end cell row blank equals 400 row AF equals cell plus-or-minus √ 400 end cell end table end style 

karena panjang sisi, maka AF non negatif sehingga begin mathsize 14px style AF equals 20 blank cm end style 

Jadi, panjang diagonal bidang begin mathsize 14px style bottom enclose bold AF bold equals bold BE bold equals bold CH bold equals bold DG bold equals bold 20 blank bold cm end enclose end style 

  • Diagonal Ruang

begin mathsize 14px style AG equals HB equals FD equals EC end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AG squared end cell equals cell AC squared plus GC squared end cell row blank equals cell 320 plus 144 end cell row blank equals 464 row AG equals cell plus-or-minus √ 464 end cell end table end style 

karena panjang sisi, maka AG non negatif sehingga undefined 

Jadi, panjang diagonal ruang begin mathsize 14px style bottom enclose bold AG bold equals bold HB bold equals bold FD bold equals bold EC bold equals bold 4 square root of bold 29 blank bold cm end enclose end style 

  • Bidang Diagonal

​​​​​​​begin mathsize 14px style EHBC equals ADGF end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript EHBC end cell equals cell straight L subscript ADGF end cell row cell straight L subscript EHBC end cell equals cell straight p cross times straight l end cell row blank equals cell EB cross times BC end cell row blank equals cell 20 cross times 8 end cell row blank equals cell 160 space cm squared end cell end table end style 

​​​​​​​Jadi, luas bidang diagonal undefined  

begin mathsize 14px style ABGH equals EFCD end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript ABGH end cell equals cell straight L subscript EFCD end cell row cell straight L subscript ABGH end cell equals cell straight p cross times straight l end cell row blank equals cell AB cross times BG end cell row blank equals cell 16 cross times 4 √ 3 end cell row blank equals cell 64 √ 13 space cm squared end cell end table end style 

Jadi, luas bidang diagonal  begin mathsize 14px style bottom enclose bold ABGH bold equals bold EFCD bold equals bold 64 square root of bold 13 blank blank bold cm to the power of bold 2 end enclose end style

begin mathsize 14px style EACG equals HDBF end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript EACG end cell equals cell straight L subscript HDBF end cell row cell straight L subscript EACG end cell equals cell straight p cross times straight l end cell row blank equals cell AC cross times CG end cell row blank equals cell 8 √ 5 cross times 12 end cell row blank equals cell 96 √ 5 space cm squared end cell end table end style 

Jadi, luas bidang diagonal ​​​​​​​begin mathsize 14px style bottom enclose bold EACG bold equals bold HDBF bold equals bold 96 square root of bold 5 blank blank bold cm to the power of bold 2 end enclose end style 

 

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