Diketahui AB = AD, DC = BC = 4 cm. Tentukan luas segiempat ABCD!

Pertanyaan

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Dengan aturan cosinus maka akan ditentukan panjang DB sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell DB squared end cell equals cell CD squared plus CB squared minus 2 times CD times CB times cos space 120 degree end cell row blank equals cell 4 squared plus 4 squared minus up diagonal strike 2 times 4 times 4 times negative fraction numerator 1 over denominator up diagonal strike 2 end fraction end cell row blank equals cell 16 plus 16 plus 16 end cell row cell DB squared end cell equals 48 end table$

Selanjutnya akan ditentukan panjang AB dengan aturan cosinus berikut.

misal AB equals straight x , maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell DB squared end cell equals cell AB squared plus AD squared minus 2 times AB times AD times cos space 60 degree end cell row 48 equals cell x squared plus x squared minus up diagonal strike 2 times x times x fraction numerator 1 over denominator up diagonal strike 2 end fraction end cell row 48 equals cell 2 x squared minus x squared end cell row 48 equals cell x squared end cell row x equals cell plus-or-minus square root of 48 end cell row x equals cell plus-or-minus 4 square root of 3 end cell end table$

Panjang AD tidak mungkin negative 4 square root of 3 space cm jadi panjang AD adalah

Luas segiempat ABCD dapat ditentukan dengan cara berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript ABCD end cell equals cell straight L subscript DCB plus straight L subscript DAB end cell row blank equals cell 1 half times DC times BC times sin space 120 degree plus 1 half times AB times AD times sin space 60 degree end cell row blank equals cell fraction numerator 1 over denominator up diagonal strike 2 end fraction times up diagonal strike 4 times 4 times fraction numerator 1 over denominator up diagonal strike 2 end fraction square root of 3 plus fraction numerator 1 over denominator up diagonal strike 2 end fraction times up diagonal strike 4 square root of 3 times 4 square root of 3 times fraction numerator 1 over denominator up diagonal strike 2 end fraction square root of 3 end cell row blank equals cell 4 square root of 3 plus 12 square root of 3 end cell row blank equals cell 16 square root of 3 space cm squared end cell end table$

Jadi, luas segiempat ABCD tersebut adalah

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