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Dari segitiga ABC, tentukan keliling dan luas segitiga ABC

Pertanyaan

Dari segitiga ABC, tentukan keliling dan luas segitiga ABCspace 


  

F. Juliano

Master Teacher

Jawaban terverifikasi

Jawaban

keliling segitiga tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 open parentheses square root of 3 plus square root of 6 plus 3 close parentheses space cm end cell end table dan luasnya adalah 5 square root of 3 space cm squared.

Pembahasan

Perhatikan gambar berikut.
 



Dengan menggunakan perbandingan panjang sisi-sisi pada segitiga siku-siku yang salah satu sudutnya begin mathsize 14px style 60 degree end style maka begin mathsize 14px style OB space colon space CO space colon space CB space equals space 1 space colon space square root of 3 space colon space 2 end style sehingga diperoleh:
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell OB space colon space CB space end cell equals cell space 1 space colon space 2 end cell row cell OB space colon space 4 space end cell equals cell space 1 space colon space 2 end cell row OB equals cell 2 space cm end cell row blank blank blank row cell CO space colon space CB end cell equals cell space square root of 3 space colon space 2 end cell row cell CO space colon space 4 end cell equals cell square root of 3 space colon space 2 end cell row CO equals cell 2 square root of 3 space cm end cell end table end style 
 

Dengan menggunakan perbandingan panjang sisi-sisi pada segitiga siku-siku yang salah satu sudutnya begin mathsize 14px style 45 degree end style maka begin mathsize 14px style AO space colon space CO space colon space AC equals 1 space colon space 1 space colon space square root of 2 end style sehingga diperoleh:
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AO space colon space CO end cell equals cell 1 space colon space 1 end cell row cell AO space colon space 2 square root of 3 end cell equals cell 1 space colon space 1 end cell row cell AO space end cell equals cell space 2 square root of 3 space cm end cell row blank blank blank row cell AO space colon thin space AC end cell equals cell 1 space colon space square root of 2 end cell row cell 2 square root of 3 space colon space AC end cell equals cell 1 space colon space square root of 2 end cell row AC equals cell 2 square root of 6 space cm end cell end table end style 
 

Dengan demikian begin mathsize 14px style AB equals AO plus BO equals 2 square root of 3 plus 2 equals 2 open parentheses square root of 3 plus 1 close parentheses space cm end style 

Keliling segitiga ABC 


begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight K subscript increment ABC end subscript end cell equals cell AB plus BC plus AC end cell row blank equals cell 2 open parentheses square root of 3 plus 1 close parentheses plus 4 plus 2 square root of 6 end cell row blank equals cell 2 square root of 3 plus 2 plus 4 plus 2 square root of 6 end cell row blank equals cell 2 square root of 3 plus 2 square root of 6 plus 6 end cell row blank equals cell 2 open parentheses square root of 3 plus square root of 6 plus 3 close parentheses space cm end cell end table end style 
 

Luas segitiga ABC


begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript increment ABC end subscript end cell equals cell 1 half cross times AB cross times CO end cell row blank equals cell 1 half cross times 2 open parentheses square root of 3 plus 1 close parentheses cross times 2 square root of 3 end cell row blank equals cell 1 half cross times 2 square root of 3 plus 2 cross times 2 square root of 3 end cell row blank equals cell 5 square root of 3 space cm squared end cell end table end style 
 

Dengan demikian, keliling segitiga tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 open parentheses square root of 3 plus square root of 6 plus 3 close parentheses space cm end cell end table dan luasnya adalah 5 square root of 3 space cm squared.

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