kubus abcd efgh mempunyai panjang rusuk 2 satuan
kubus abcd efgh mempunyai panjang rusuk 2 satuan

kubus abcd efgh mempunyai panjang rusuk 2 satuan

Perhatikan gambar kubus ABCD.EFGH berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell Misal colon end cell row blank blank cell S space titik space tengah space E H end cell row blank blank cell Q space titik space tengah space B C end cell row blank blank cell P space titik space tengah space S Q end cell row blank blank blank row cell Q S end cell equals cell B E equals C H equals diagonal space sisi space kubus end cell row blank blank cell Maka colon end cell row cell Q S end cell equals cell s square root of 2 equals 2 square root of 2 end cell row blank blank cell Sehingga colon end cell row cell P Q end cell equals cell 1 half cross times Q S end cell row blank equals cell 1 half cross times 2 square root of 2 end cell row blank equals cell square root of 2 end cell row blank blank blank row cell O Q end cell equals cell 1 half cross times F B end cell row blank equals cell 1 half cross times 2 end cell row blank equals 1 row blank blank blank row cell O P end cell equals cell 1 half cross times A B end cell row blank equals cell 1 half cross times 2 end cell row blank equals 1 end table end style

Perhatikan segitiga siku-siku PQO, jarak titik O ke bidang BCHE adalah OR.

Pada segitiga PQO siku-siku di titik O.

  • Jika alasnya OP maka tingginya OQ
  • Jika alasnya PQ maka tingginya OR

Dengan kesamaan luas segitiga, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 1 half cross times P Q cross times O R end cell equals cell 1 half cross times O P cross times O Q end cell row cell 1 half cross times square root of 2 cross times O R end cell equals cell 1 half cross times 1 cross times 1 end cell row cell fraction numerator square root of 2 over denominator 2 end fraction cross times O R end cell equals cell 1 half end cell row cell fraction numerator square root of 2 over denominator 2 end fraction cross times O R divided by fraction numerator square root of 2 over denominator 2 end fraction end cell equals cell 1 half divided by fraction numerator square root of 2 over denominator 2 end fraction end cell row cell O R end cell equals cell 1 half cross times fraction numerator 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator square root of 2 over denominator 2 end fraction space satuan end cell end table end style

Jadi, jawaban yang tepat adalah D.

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