Makalah Bangun Datar
NAMA:SRI MARHANI KELAS: XI Akuntansi II Pembimbing:DIDI HARIYANTO NISN: 9976630436 NIS:01312
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Kata pengantar Puji dan syukur kami panjatkan kehadirat Tuhan yang maha esa atas segala limpahan rahmat dan hidayah nya Sehingga kami dapat menyelesaikan tugas makalah yang berjudul Bangun Datar ini dengan sebaik-baiknya. Kami sadar bahwa makalah ini tidak dapat terselesaikan dengan baik tanpa bantuan guru dan pihak-pihak yang telah membantu baik secara moril maupun spiritual untuk itu kami mengucapkan terima kasih. Dan harapan kami semoga makalah ini dapat bermanfaat bagi semua pihak. “Tiada Gading yang tak retak” pepatah itulah yang mewakili mewakili ungkapan perasaan kami kami
bahwa makalah in jauh dari sempurna,maka kiranya kritik dan saran sangat kami nanti dari pembaca
Jambi, Mei 2014
penulis
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pendahuluan pengertian bangun datar
bangun datar adalah bagian dari bidang datar yang dibatasi oleh garis-garis lurus atau lengkung (Imam Roji,1997). bangun datar dapat di defenisikan sebagai bangun yang rata yang mempunyai dua dimensi yaitu panjang dan lebar,tetapi tidak mempunyai tinggi atau tebal (Julius Hambali,Siskandar,dan Muhamad Rohmad,1996) berdasarkan pengertian tersebut dapat ditegaskan bahwa bangun datar merupakan merupakan banun dua dimensi dimensi yang hanya memiliki panjang dan lebar yang dibatasi oleh garis lurus atau lengkung.
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1.PERSEGI A.PENGERTIAN PERSEGI datar dua dimensi yang dibentuk oleh empat buah rusuk buah rusuk Persegi adalah bangun datar dua panjang dan memiliki empat buah sudut buah sudut yang kesemuanya adalah sudut adalah sudut siku-siku
B.SIFAT SIFAT PERSEGI
Pada bangun datar persegi, mempunyai sifat-sifat diantaranya :
Memiliki 4 sisi dan 4 titik sudut
Memiliki 2 pasang sisi yang sejajar dan sama panjang
Keempat sisinya sama panjang
Keempat Sudutnya sama besar yaitu 90 derajat (siku-siku)
Memiliki 4 simetri lipat
Memiliki simetri putar tingkat 4
C.RUMUS PERSEGI
Rumus Persegi Luas = s x s = s 2 Keliling = 4 x s dengan s = panjang sisi persegi D.CONTOH SOAL PERSEGI a. Keliling persegi
contoh: keliling persegi 24 cm, berapa cm panjang sisinya jawab: keliling = 4 x s = 24 cm sisi= 24 cm : 4= 6 cm Jadi, panjang sisinya = 6 cm b. Luas persegi
contoh : sebuah persegi sisinya 5 cm. tentukan luasnya! jawab : Luas = s x s = 5 cm x 5 cm
yang sama
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2.PERSEGI PANJANG A.PENGERTIAN PERSEGI PANJANG datar dua dimensi yang dibentuk oleh dua Persegi panjang (inggris rectangle) adalah bangun datar dua pasang rusuk pasang rusuk yang masing-masing sama panjang dan sejajar dan sejajar dengan pasangannya, dan memiliki empat buah sudut buah sudut yang kesemuanya adalah sudut adalah sudut siku-siku.
B.SIFAT SIFAT PERSEGI Pada bangun datar persegi panjang, mempunyai sifat-sifat diantaranya :
Memiliki 4 sisi dan 4 titik sudut
Memiliki 2 pasang sisi sejajar, berhadapan dan sama panjang
Memiliki 4 sudut yang besarnya 90 derajat
Keempat sudutnya siku-siku
Memiliki 2 diagonal di agonal yang sama panjang
Memiliki 2 simetri lipat
Memiliki Simetri putar tingkat 2
C.RUMUS PERSEGI PANJANG
Rumus Persegi Panjang Luas = p x l p = Luas : lebar l = Luas : panjang Keliling = 2p + 2l = 2 x (p + l) dengan p = panjang persegi panjang, dan l = lebar persegi panjang D.CONTOH SOAL PERSEGI PANJANG Diketahui panjang dari ( p) 5 cm dan lebar nya ( l ) adalah 4 cm,
Persegi
panjang
di
bawah
adalah
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a.Luas b.Keliling Diketahui: p=5cm l =4cm Jawab: a.Luas Persegi Panjang
Penyelesaian: L=pxl =5x4 =20 Jadi luas persegi panjang tsb adalah 20 cm
b. Keliling Persegi panjang
K = 2 x ( p + l ) =2x(5+4) =2x(9) = 18 cm jadi keliling Persegi panjang tsb tsb adalah 18 cm.
3.SEGITIGA A.PENGERTIAN SEGITIGA Segitiga atau segi tiga adalah nama suatu bentuk yang dibuat dari tiga sisi yang berupa garis lurus dan tiga sudut. tiga sudut. B.SIFAT-SIFAT SEGITIGA
Pada bangun datar Segitiga, mempunyai sifat-sifat diantaranya :
Mempunyai 3 sisi dan 3 titik sudut Jumlah ketiga sudutnya 180 derajat
C.JENIS JENIS SEGITIGA 1. Jenis segitiga ditinjau dari panjang sisi-sisinya : a. Segitiga Sembarang
Segitiga sembarang adalah segitiga yang ketiga sisinya berbeda panjangnya dan ketiga sudutnya berbeda besarnya.
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b. Segitiga Sama kaki
Segitiga sama kaki adalah segitiga yang dua dari tiga sisinya sama panjang.
c. Segitiga Sama sisi
Segitiga sama sisi adalah segitiga yang ketiga sisinya sama panjang.
2. Jenis segitiga ditinjau dari besar sudut-sudutnya : a. Segitiga Lancip
Segitiga lancip adalah segitiga yang ketiga sudutnya merupakan sudut lancip atau besar sudutnya antara 0 o dan 90o .
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Segitiga siku-siku adalah segitiga yang salah satu sudutnya siku –siku atau besar sudutnya 90 o.
c. Segitiga Tumpul
Segitiga tumpul adalah segitiga yang satu dari tiga sudutnya merupakan sudut tumpul atau besar sudutnya antara 90 o dan 180o.
3. Segitiga Istimewa
Segitiga istimewa merupakan segitiga yang memiliki sifat-sifat khusus (istimewa), baik mengenai hubungan panjang sisi-sisinya maupun hubungan besar sudut-sudutnya. Yang merupakan segitiga istimewa di antara jenis-jenis segitiga adalah : - Segitiga siku-siku - Segitiga sama kaki - Segitiga sama sisi
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1.Pada gambar di bawah ini, panjang AB = 10 cm, BC = 8 cm, dan AC = 9 cm. Hitunglah keliling segitiga itu?
Penyelesaian: KelilingΔ ABC = AB + BC + AC
= 10 + 8 + 9 = 27 cm 2. Hitunglah luas segitiga pada gambar di bawah ini.
Penyelesaian: Luas Δ = ½ x a x t a. diketahui: a.alas =18 b.tinggi=12
= ½ x 18 x 12 =108 cm²
b. diketahui: diketahui: a.alas =10 b.tinggi=9
= ½ x 10 x 9 =45 cm²
4.JAJAR GENJANG
A.PENGERTIAN JAJAR GENJANG
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Memiliki 4 sisi dan 4 titik sudut
Memiliki 2 pasang sisi yang sejajar dan sama panjang
Memiliki 2 sudut tumpul dan 2 sudut lancip
Sudut yang berhadapan sama besar
Diagonalnya tidak sama panjang
Tidak memiliki simetri lipat
Memiliki simetri putar tingkat 2
Rumus jajar genjang
C.RUMUS JAJAR GENJANG
Rumus jajar genjang Luas = a x t Keliling = AB + BC + CD + AD D.CONTOH SOAL JAJAR GENJANG
Contoh Soal:
ABCD adalah jajargenjang dengan AB = 10 cm, BC = 8 cm, dan DE = 6 cm. Tentukanlah luas jajargenjang tersebut. Penyelesaian:
Luas jajargenjang = alas × tinggi = 10 cm × 6 cm = 60 cm2 2.Sebuah jajargenjang mempunyai panjang = 7 cm dan lebar = 5 cm dan tinggi = 4 cm berapa keliling jajar genjang tersebut
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=24 cm
5.TRAPESIUM a.pengertian trapesium b.sifat sifat trapesium
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Luas = (Jumlah sisi Sejajar) X t : 2 Keliling = AB + BC + CD + AD
d.contoh soal trapesium Contoh Soal: Pada gambar berikut, ABCD adalah trapesium sama kaki kaki dengan AD = BC = DC = 10 cm, DE = 8 cm, dan AB = 2 × DC. Hitunglah keliling dan luasnya.
Penyelesaian: AD = BC = DC = 10 cm AB = 2 × DC = 2 × 10 cm = 20 cm Keliling = AB + BC BC + DC + AD = 20 + 10 + 10 + 10 = 50 cm Luas= jumlah sisi sejajar x t:2 Luas = (10 + 20) x 8 =240=120cm2 2 2
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6.Layang layang a.pengertian layang layang b.sifat layang layang Pada bangun datar Layang - Layang, mempunyai sifat-sifat diantaranya :
Memiliki 4 sisi dan 4 titik sudut
Memiliki 2 pasang sisi yang sama panjang
Memiliki 2 sudut yang sama besar
Diagonalnya berpotongan tegak lurus
Salah satu diagonalnya membagi diagonal yang lain sama panjang
Memiliki 1 simetri lipat.
c.rumus layang- layang Luas = ½ x diagonal 1 X diagonal2 Keliling = AB + BC + CD + AD
d.contoh soal layang-layang
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7.belah ketupat a.pengertian lingkaran b.sifat-sifat belah ketupat Pada bangun datar Belah Ketupat, mempunyai sifat-sifat diantaranya :
Memiliki 4 sisi dan 4 titik sudut
Keempat sisinya sama panjang
Memiliki 2 pasang sudut yang berhadapan sama besar
Diagonalnya berpotongan tegak lurus
Memiliki 2 simetri lipat
Memiliki simetri putar tingkat 2
c.rumus belah ketupat Luas = ½ X diagonal 1 X diagonal2 Keliling = AB + BC + CD + AD
d.contoh soal belah ketupat Contoh Soal
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Keliling = 4 x sisi = 4 x 5 cm = 20 cm
5cm
5cm
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8.Lingkaran a.pengertian lingkaran Lingkaran adalah bangun datar yang terbentuk terbentuk dari himpunan semua titik persekitaran yang mengelilingi suatu titik asal dengan jarak yang sama. jarak tersebut biasanya dinamakan r, atau radius, atau jari-jari.
b.sifat-sifat lingkaran Pada bangun datar Lingkaran, mempunyai sifat-sifat diantaranya :
Mempunyai 1 sisi
Memiliki simetri putar dan simetri lipat tak terhingga
c.Rumus lingkaran luas= π x r2 Keliling = 2 x π x r d.contoh soal
1.Diketahui sebuah ban sepeda motor yang berbentuk lingkaran memiliki jari jari 3,5 cm, berapakah keliling
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L = (22/7) x 142 L = 22 x 2 x 14 m2 L = 616 m2
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penutup Demikianlah makalah tentang “Bangun Datar” yang kami buat ini,semoga bermanfaat dan menambah ilmu pengetahuan para pembaca. Dan saya mohon maaf apabila ada kesalahan ejaan dalam penulisan kata dan kalimat yang kurang jelas,dimengerti dan lugas ,karena kami hanyalah manusia biasa yang tak luput dari kesalahan dan saya juga sangat mengharap kan saran dan kritik dari pembaca demi kesempurnaan makalah ini. Sekian penutup dari saya semoga dapat diterima dihati dan saya ucapkan terima kasih sebesar besar nya WassalamualaikumWr.Wb.