Perhatikan balok ABCD.EFGH berikut ini! Tentukan: b. Panjang diagonal ruang.

Pertanyaan

Perhatikan balok ABCD.EFGH berikut ini!

Tentukan:

b. Panjang diagonal ruang.

P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

luas bidang diagonal balok tersebut masing-masing adalah Error converting from MathML to accessible text..

Pembahasan

Berdasarkan gambar yang diberikan di atas, diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row AB equals cell 12 space cm end cell row cell B C end cell equals cell 4 space cm end cell row CG equals cell 6 space cm end cell end table 

Bidang diagonal balok terdiri dari 6 bidang sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row EBCH equals ADGF row EFCD equals ABGH row ACGE equals BDHF end table 

Untuk menentukan luasnya, terlebih dahulu ditentukan panjang diagonal bidang yaitu BE, BG, dan AC sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row BE equals cell square root of AB squared plus AE squared end root end cell row blank equals cell square root of AB squared plus CG squared end root end cell row blank equals cell square root of 12 squared plus 6 squared end root end cell row blank equals cell square root of 144 plus 36 end root end cell row blank equals cell square root of 180 end cell row blank equals cell square root of 36 middle dot 5 end root end cell row blank equals cell 6 square root of 5 space cm end cell row blank blank blank row BG equals cell square root of B C squared plus CG squared end root end cell row blank equals cell square root of 4 squared plus 6 squared end root end cell row blank equals cell square root of 16 plus 36 end root end cell row blank equals cell square root of 52 end cell row blank equals cell square root of 4 middle dot 13 end root end cell row blank equals cell 2 square root of 13 space cm end cell row blank blank blank row AC equals cell square root of AB squared plus B C squared end root end cell row blank equals cell square root of 12 squared plus 4 squared end root end cell row blank equals cell square root of 144 plus 16 end root end cell row blank equals cell square root of 160 end cell row blank equals cell square root of 16 middle dot 10 end root end cell row blank equals cell 4 square root of 10 space cm end cell end table  

Sehingga dapat ditentukan luas masing-masing bidang diagonal balok di atas sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell L subscript EBCH end cell equals cell L subscript ADGF end cell row blank equals cell B C middle dot BE end cell row blank equals cell 4 middle dot 6 square root of 5 end cell row blank equals cell 24 square root of 5 space cm squared end cell row blank blank blank row cell L subscript EFCD end cell equals cell L subscript ABGH end cell row blank equals cell AB middle dot BG end cell row blank equals cell 12 middle dot 2 square root of 13 end cell row blank equals cell 24 square root of 13 space cm squared end cell row blank blank blank row cell L subscript ACGE end cell equals cell L subscript BDHF end cell row blank equals cell CG middle dot AC end cell row blank equals cell 6 middle dot 4 square root of 10 end cell row blank equals cell 24 square root of 10 space cm squared end cell end table  

Jadi, luas bidang diagonal balok tersebut masing-masing adalah Error converting from MathML to accessible text..

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