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

Pertanyaan

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

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 4 square root of 3 space cm 

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 16 square root of 3 space end root space cm squared

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