Roboguru

Pertanyaan

Perhatikan gambar berikut.

ABCD persegi dengan panjang sisi-siinya adalah begin mathsize 14px style 2 space cm end style. E adalah titik tengah CD dan F adalah titik tengah CD dan F adalah titik tengah AD. Luas daerah EDFGH adalah … begin mathsize 14px style cm squared end style 

(OSK SMP 2011)

  1. ...undefined 

  2. ...undefined 

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

Luas daerah EDFGH adalah begin mathsize 14px style 4 over 3 space cm squared end style

Pembahasan

Luas yang kita cari adalah daerah yang diarsir pada gambar berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell B D squared end cell equals cell C D squared plus B C squared end cell row blank equals cell 2 squared plus 2 squared end cell row blank equals cell 8 space cm end cell row blank blank blank row cell B D end cell equals cell 2 square root of 2 space cm end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell B O end cell equals cell 1 half B D end cell row blank equals cell 1 half open parentheses 2 square root of 2 close parentheses end cell row blank equals cell square root of 2 space cm end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A C end cell equals cell B D end cell row blank equals cell 2 square root of 2 space cm end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell G H end cell equals cell 1 third A C end cell row blank equals cell 1 third cross times 2 square root of 2 end cell row blank equals cell 2 over 3 square root of 2 space cm end cell end table end style


begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell L subscript E D F G H end subscript end cell equals cell L subscript A B C D end subscript minus L subscript B C E end subscript minus L subscript A B F end subscript minus L B G H end cell row blank equals cell C D cross times B C minus fraction numerator C E cross times C B over denominator 2 end fraction minus fraction numerator A B cross times A F over denominator 2 end fraction minus fraction numerator G H cross times B O over denominator 2 end fraction end cell row blank equals cell 2 cross times 2 minus fraction numerator 1 cross times 2 over denominator 2 end fraction minus fraction numerator 2 cross times 1 over denominator 2 end fraction minus fraction numerator open parentheses begin display style bevelled 2 over 3 end style close parentheses square root of 2 cross times square root of 2 over denominator 2 end fraction end cell row blank equals cell 4 minus 1 minus 1 minus 2 over 3 end cell row blank equals cell 2 minus 2 over 3 end cell row blank equals cell 4 over 3 space cm squared end cell end table end style

Jadi, Luas daerah EDFGH adalah begin mathsize 14px style 4 over 3 space cm squared end style

14

0.0 (0 rating)

Pertanyaan serupa

Hitunglah luas daerah bangun di samping!

12

0.0

Jawaban terverifikasi

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

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia