Berapa Luasnya – I

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, 07-04-2020

Published by Hendra Gunawan

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

4 Comments

  1. luas daerah biru = luas 1 buah lingkaran berjari-jari setengah satuan +luas 1 buah lingkaran berjari-jari 1/4 satuan =phi x (1/2)^2 +phi (1/4)^2=5/16 phi

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  2. Luas 4 bagian = π(½)²=¼π
    Diameter lingkaran =√2 -2(½)=√2-1
    Luas lingkaran =¼π(√2-1)²=¼π(3-2√2)
    Luas total=(1-½√2)π= 0,9201511845

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  3. Izin menjawab,
    Luas 4.¼lingkaran besar= ¼.4.πr²=π.(½)²=π/4 sat luas
    Diagonal=√2
    Jari-jari kecil= ½(√2-1)
    Luas lingkaran kecil=π(½(√2-1))²=π((3-2√2)/4) sat luas
    Luas total daerah biru= ¼π+((3-2√2)/4)π=¼π(4-2√2)=(1-½√2)π sat luas

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