Sebuah layang-layang dengan diagonal pendek AC dan diagonal panjang BD berpotongan di E. Jika panjang DE = 8 cm, AC = 12 cm, dan BC = 3CD, tentukan keliling dan luas layang-layang tersebut!

Pertanyaan

Sebuah layang-layang dengan diagonal pendek AC dan diagonal panjang BD berpotongan di E. Jika panjang DE = 8 space cm, AC = 12 space cm, dan BC = 3 CD, tentukan keliling dan luas layang-layang tersebut!

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

keliling dan luas layang-layang tersebut berturut-turut adalah 80 space cm dan 48 plus 72 square root of 6 space cm squared  

Pembahasan

Diketahui : DE = 8 space cm, AC = 12 space cm, dan BC = 3 CD

Ilutrasi gambarnya yaitu 

Panjang AC = 12 space cm maka panjang EC = AC over 2 equals 12 over 2 equals 6 space cm 

Cari panjang CD menggunakan teorema pythagorasspace 

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis CD right parenthesis squared end cell equals cell left parenthesis EC right parenthesis squared plus left parenthesis ED right parenthesis squared left parenthesis CD right parenthesis squared equals 6 squared plus 8 squared end cell row CD equals cell square root of 6 squared plus 8 squared end root end cell row CD equals cell square root of 36 plus 64 end root end cell row CD equals cell square root of 100 end cell row CD equals 10 end table 

Diketahui BC = 3CD maka BC equals 3 cross times CD equals 3 cross times 10 equals 30 space cm sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row Keliling equals cell 10 cross times 2 plus 30 cross times 2 end cell row blank equals cell 20 plus 60 end cell row blank equals 80 end table 

Cari panjang EB menggunakan teorema pythagorasspace 

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis EB right parenthesis squared end cell equals cell left parenthesis BC right parenthesis squared minus left parenthesis EC right parenthesis squared space end cell row cell left parenthesis EB right parenthesis squared end cell equals cell 30 squared minus 6 squared end cell row EB equals cell square root of 30 squared minus 6 squared end root end cell row EB equals cell square root of 900 minus 36 end root end cell row EB equals cell square root of 864 end cell row EB equals cell square root of 144 cross times 6 end root end cell row EB equals cell square root of 12 squared cross times 6 end root end cell row EB equals cell 12 square root of 6 end cell end table  

Rumus luas layang-layang adalah fraction numerator straight d subscript 1 cross times straight d subscript 2 over denominator 2 end fraction maka

table attributes columnalign right center left columnspacing 0px end attributes row straight L equals cell fraction numerator straight d subscript 1 cross times straight d subscript 2 over denominator 2 end fraction end cell row straight L equals cell fraction numerator 12 cross times left parenthesis 8 plus 12 square root of 6 right parenthesis over denominator 2 end fraction end cell row blank equals cell fraction numerator 96 plus 144 square root of 6 over denominator 2 end fraction end cell row blank equals cell 48 plus 72 square root of 6 end cell end table 

Jadi, keliling dan luas layang-layang tersebut berturut-turut adalah 80 space cm dan 48 plus 72 square root of 6 space cm squared  

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