kubus abcd efgh mempunyai panjang rusuk 2 satuan

Editor 11 Juni 2022 Leave a comment 24 Views

Perhatikan gambar kubus ABCD.EFGH berikut!

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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