Roboguru

Pada gambar disamping, diketahui panjang  dan     ...

Pada gambar disamping, diketahui panjang begin mathsize 14px style BD equals 6 space cm end style dan begin mathsize 14px style BC equals 14 space cm end style 
 

 
 

Hitunglah luas begin mathsize 14px style increment ABC end style

Jawaban:

Perhatikan segitiga begin mathsize 14px style bold ABC end style dan segitiga begin mathsize 14px style bold ABD end style . begin mathsize 14px style increment ABC tilde increment ABD end style 

Dengan menggunakan konsep kesebangunan diperoleh
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell AB over BD end cell equals cell BC over AB end cell row cell AB cross times AB end cell equals cell BD cross times BC end cell row cell AB squared end cell equals cell BD cross times BC end cell end table end style

  

Selanjutnya kita tentukan panjang  panjang begin mathsize 14px style AB end style 
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell AB squared end cell equals cell BD cross times BC end cell row cell AB squared end cell equals cell 6 cross times 14 end cell row cell AB squared end cell equals 84 row AB equals cell square root of 84 end cell row AB equals cell 2 square root of 21 space cm end cell end table end style 
 

diperoleh panjang  begin mathsize 14px style AB end style  yaitu begin mathsize 14px style 2 square root of 21 space cm end style 

Selanjutnya kita tentukan tinggi segitiga yaitu panjang begin mathsize 14px style AC end style dengan menggunakan teorema phytagoras;
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row AC equals cell square root of BC squared minus AB squared end root end cell row blank equals cell square root of 14 squared minus open parentheses square root of 84 close parentheses squared end root end cell row blank equals cell square root of 196 minus 84 end root end cell row blank equals cell square root of 112 end cell row blank equals cell 4 square root of 7 space cm end cell end table end style 

 

diperoleh panjang begin mathsize 14px style AC end style  yaitu begin mathsize 14px style 4 square root of 7 space cm end style 

Sehingga luas begin mathsize 14px style increment ABC end style
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight L increment ABC end cell equals cell 1 half cross times alas cross times tingii end cell row blank equals cell 1 half cross times AB cross times AC end cell row blank equals cell 1 half cross times 2 square root of 21 cross times 4 square root of 7 end cell row blank equals cell square root of 21 cross times 4 square root of 7 end cell row blank equals cell 4 cross times square root of 147 end cell row blank equals cell 4 cross times 7 square root of 3 end cell row blank equals cell 28 square root of 3 space cm squared end cell end table end style 
 

Jadi, luas begin mathsize 14px style increment ABC end style adalah begin mathsize 14px style 28 square root of 3 space cm squared end style 

0

Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved