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Nilai pecahan yang ditunjukkan oleh bagian yang diarsir adalah ....

Pertanyaan

Nilai pecahan yang ditunjukkan oleh bagian yang diarsir adalah .... 

  1. 4 over 9 

  2. 7 over 12 

  3. 5 over 12 

  4. 5 over 8 

Pembahasan Soal:

Ingat kembali:

straight L subscript straight p. panjang end subscript equals straight p cross times straight l straight L subscript segitiga equals 1 half cross times straight a cross times straight t 

Dari gambar yang diberikan, dapat di ubah sebagai berikut:

Maka:

- Menentukan Luas Total

table attributes columnalign right center left columnspacing 0px end attributes row cell Luas space total end cell equals cell straight L subscript straight p. panjang end subscript end cell row blank equals cell p cross times l end cell row blank equals cell 3 a cross times 2 a end cell row blank equals cell 6 a squared end cell end table 

- Menentukan luas arsir

table attributes columnalign right center left columnspacing 0px end attributes row cell Luas space arsir end cell equals cell Luas space total minus open parentheses straight L subscript straight I plus straight L subscript II plus straight L subscript III close parentheses end cell row blank equals cell 6 a squared minus open parentheses straight L subscript segitiga space straight I end subscript plus straight L subscript segitiga space II end subscript plus straight L subscript segitiga space III end subscript close parentheses end cell row blank equals cell 6 a squared minus open parentheses 1 half times a times t plus 1 half times a times t plus 1 half times a times t close parentheses end cell row blank equals cell 6 a squared minus open parentheses fraction numerator 1 over denominator up diagonal strike 2 end fraction times a times up diagonal strike 2 a plus 1 half times a times 3 a plus fraction numerator 1 over denominator up diagonal strike 2 end fraction times a times up diagonal strike 2 a close parentheses end cell row blank equals cell 6 a squared minus open parentheses a squared over 2 plus fraction numerator 3 a squared over denominator 2 end fraction plus a squared over 2 close parentheses end cell row blank equals cell 6 a squared minus fraction numerator 5 a squared over denominator 2 end fraction end cell row blank equals cell fraction numerator 12 a squared over denominator 2 end fraction minus fraction numerator 5 a squared over denominator 2 end fraction end cell row blank equals cell fraction numerator 7 a squared over denominator 2 end fraction end cell end table 

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell Pecahan space daerah space arsir end cell equals cell fraction numerator Luas space arsir over denominator Luas space total end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 7 a squared over denominator 2 end fraction end style over denominator 6 a squared end fraction end cell row blank equals cell fraction numerator 7 a squared over denominator 2 end fraction cross times fraction numerator 1 over denominator 6 a squared end fraction end cell row blank equals cell fraction numerator 7 up diagonal strike a squared end strike over denominator 12 up diagonal strike a squared end strike end fraction end cell row blank equals cell 7 over 12 end cell end table 

Jadi, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Juli 2021

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