Berapa Luasnya – II

Hendra Gunawan


Bila luas daerah persegi dalam gambar di bawah ini sama dengan 1 satuan luas, berapa luas daerah yang berwarna biru?

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Bandung, 11-04-2020

Published by Hendra Gunawan

I'm a professor of mathematics at the Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia.

3 Comments

  1. Izin menjawab prof. mohon koreksinya,
    Luas lingkaran besar=π(1/2)²=1/4 π
    Diameter lingkaran kecil=½(√2 -1).
    Luas lingkaran kecil = ¼π(½(√2-1))²=1/16 π(3-2√2)
    Luas total= (¼+¾-½√2)π =(1-√2)π≈0,9201511845

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  2. Luas lingkaran besar biru=πr²=π.(½)²=¼π sat luas
    Diagonal=√2 sat panjang
    Mencari diameter lingkaran biru kecil:
    1+2x+x(√2-1)=√2
    (2-1+√2)x=√2-1
    (1+√2)x=√2-1
    x=(√2-1)/(√2+1) satuan panjang
    Jari2 lingkaran biru kecil=(√2-1)/(2√2+2)
    Luas 4 lingkaran biru kecil=4πr²=4π((√2-1)/(2√2+2))²=2π(√2-1)/(√2+1) satuan luas

    Luas total daerah biru= ¼π((9√2-7)/(√2+1)) satuan luas

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