Pertanyaan

Diketahui segi-8 beraturan dengan panjang jari-jari lingkaran luar r cm. Panjang sisi segi-8 tersebut adalah....

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

$M a k a space b e s a r space s u d u t space alpha equals 360 to the power of o over 8 equals 45 to the power of o S e h i n g g a space p a d a space s e g i t i g a space O E F comma space d e n g a n space O space a d a l a h space p u s a t space l i n g k a r a n comma cos invisible function application alpha equals fraction numerator O E squared plus O F squared minus E F squared over denominator 2 cross times O E cross times O F end fraction cos invisible function application 45 to the power of o equals fraction numerator r squared plus r squared minus E F squared over denominator 2 cross times r cross times r end fraction 1 half square root of 2 equals fraction numerator r squared plus r squared minus E F squared over denominator 2 cross times r cross times r end fraction fraction numerator 1 over denominator square root of 2 end fraction equals fraction numerator 2 r squared minus E F squared over denominator 2 r squared end fraction 2 r squared equals 2 square root of 2 r squared minus E F squared square root of 2 E F squared square root of 2 equals 2 square root of 2 r squared minus 2 r squared E F squared equals fraction numerator 2 square root of 2 r squared minus 2 r squared over denominator square root of 2 end fraction E F squared equals fraction numerator left parenthesis 2 square root of 2 minus 2 right parenthesis r squared over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals fraction numerator left parenthesis 4 minus 2 square root of 2 right parenthesis r squared over denominator 2 end fraction equals left parenthesis 2 minus square root of 2 right parenthesis r squared E F squared equals left parenthesis 2 minus square root of 2 right parenthesis r squared E F equals square root of left parenthesis 2 minus square root of 2 right parenthesis r squared end root E F equals r square root of open parentheses 2 minus square root of 2 close parentheses end root$

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