Persegi & Persegi Panjang ( Rumadi )

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2. CONTOH :
Sebuah persegi panjang berukuran panjang = ( 3x + 4 ) cm , lebar = ( x + 6 ) , dan keliling = 80 cm. Tentukan luas persegi panjang tersebut. Diketahui : p = ( 3x + 4 ) cm                          l = ( x + 6 ) cm
                 l = ( x + 6 ) cm                             l = ( 5 + 6 ) cm
                 K = 80 cm                                    l = 11 cm
Ditanya    : L = .... ?
Jawab      : K = 2 ( p + l )                              p = ( 3x + 4 ) cm
                80 = 2 ( 3x + 4 + x + 6 )              p = ( 3.5 + 4 ) cm
                 80 = 2 ( 4x + 10 )                         p = ( 15 + 4 ) cm
                  80 = 8x + 20                                 p = 19 cm
                  80 - 20 = 8x
                  40 = 8x                                          Jadi : L = p x l
                  40 : 8 = x                                                L = 19 x 11
                  5 cm = x                                                  L = 209 cm ²SOAL :
Sebuah persegi panjang berukuran panjang = ( 2x - 5 ) cm , lebar = ( 3x + 11 ) , dan keliling = 72 cm. Tentukan luas persegi panjang tersebut

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Explanation

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3. CONTOH :
Diketahui luas persegi sama dengan luas persegi panjang dengan panjang = 16 cm dan lebar = 4 cm. Tentukan keliling persegi tersebut.
Diketahui : L persegi = L persegi panjang
                 p = 16 cm
                 l = 4 cm
Ditanya : K persegi = ... ?
Jawab    : L persegi = L persegi panjang
                    s ²      = p x l              Jadi :
                    s ²      =  16 x 4           K persegi = 4s
                    s ²      = 64 cm ²K persegi = 4(8)
                    s       = √ 64 cm ²K persegi = 32 cm
s       = 8 cm

SOAL :
Diketahui keliling persegi sama dengan luas persegi panjang dengan panjang = 12 cm dan lebar = 10 cm. Tentukan luas persegi tersebut.

The given answer states that the area of the square is 900 square cm. This can be calculated by using the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is given as 12 cm and the width is given as 10 cm. Therefore, the area of the rectangle is 12 cm x 10 cm = 120 cm^2. Since the area of a square is equal to the side length squared, the side length of the square is the square root of 120 cm^2, which is approximately 10.95 cm. Finally, the area of the square is the side length squared, which is approximately 10.95 cm x 10.95 cm = 120 cm^2.

Explanation

The given answer states that the area of the square is 900 square cm. This can be calculated by using the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is given as 12 cm and the width is given as 10 cm. Therefore, the area of the rectangle is 12 cm x 10 cm = 120 cm^2. Since the area of a square is equal to the side length squared, the side length of the square is the square root of 120 cm^2, which is approximately 10.95 cm. Finally, the area of the square is the side length squared, which is approximately 10.95 cm x 10.95 cm = 120 cm^2.

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4. CONTOH :
Keliling suatu persegi panjang adalah 72 cm dan lebarnya 8 cm kurang dari panjangnya. Hitunglah luas persegi panjang tersebut
Diketahui : K = 72 cm
                  l = p - 8 cm
Ditanya    : L = .... ?
Jawab      : K = 2 ( p + l )                     l = p - 8
                   72 = 2 ( p + p - 8 )             l = 22 - 8
                   72 : 2 = ( 2p - 8 )               l = 14 cm
                    36 = 2p - 8
                    36 + 8 = 2p                      Jadi L = p x l
                    44 = 2p                                   L = 22 x 14
                    44 : 2 = p                                L = 308 cm ²                    22 cm = p

SOAL :
Keliling suatu persegi panjang adalah 52 cm dan lebarnya 12 cm lebih dari panjangnya. Hitunglah luas persegi panjang tersebut

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Explanation

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6. CONTOH :
Sebuah lantai berbentuk persegi dengan panjang sisinya 6 m. Lantai tersebut akan dipasang ubin berbentuk persegi berukuran 30 cm x 30 cm. Berapa banyak ubin yang dibutuhkan untuk menutup lantai tersebut

Diketahui : s lantai = 6 m = 600 cm
                 s ubin = 30 cm
Ditanya    : banyak ubin yang dibutuhkan untuk lantai tsb ?
Jawab      : L lantai = s ²L ubin = s ²L lantai = 600 ²L ubin = 30 ²L lantai = 360.000            L ubin = 900
Jadi banyak ubin yang dibutuhkan untuk lantai tsb adalah
360.000 : 900 = 400 buah

SOAL :
Sebuah lantai berbentuk persegi panjang, dengan panjang 6 m, dan lebar = 9 m. Lantai tersebut akan dipasang ubin berbentuk persegi berukuran 30 cm x 30 cm. Berapa banyak ubin yang dibutuhkan untuk menutup lantai tersebut

The correct answer is 600. The area of the floor is calculated by multiplying the length and width, which is 6m x 9m = 54 square meters. Since each tile is 30cm x 30cm, we need to convert the area of the floor to square centimeters, which is 54m² x 10,000 = 540,000 square centimeters. To find the number of tiles needed, we divide the area of the floor by the area of each tile, which is 540,000 square centimeters / 900 square centimeters = 600 tiles. Therefore, 600 tiles are needed to cover the floor.

Explanation

The correct answer is 600. The area of the floor is calculated by multiplying the length and width, which is 6m x 9m = 54 square meters. Since each tile is 30cm x 30cm, we need to convert the area of the floor to square centimeters, which is 54m² x 10,000 = 540,000 square centimeters. To find the number of tiles needed, we divide the area of the floor by the area of each tile, which is 540,000 square centimeters / 900 square centimeters = 600 tiles. Therefore, 600 tiles are needed to cover the floor.

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7. Tentukan keliling bangun dibawah ini

The given answer states that the perimeter of the figure is 44 cm. This means that the sum of all the sides of the figure is equal to 44 cm. However, without any information about the shape or dimensions of the figure, it is not possible to determine the actual perimeter. Therefore, the given answer is incorrect and cannot be considered as a valid explanation.

Explanation

The given answer states that the perimeter of the figure is 44 cm. This means that the sum of all the sides of the figure is equal to 44 cm. However, without any information about the shape or dimensions of the figure, it is not possible to determine the actual perimeter. Therefore, the given answer is incorrect and cannot be considered as a valid explanation.

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8.

SIFAT - SIFAT PERSEGI DAN PERSEGI PANJANG
1. PERSEGI PANJANG
    Persegi panjang adalah bangun datar segi empat yang memiliki dua pasang
     sisi sejajar dan memiliki empat sudut siku-siku.
    a. Mempunyai empat sisi, dengan sepasang sisi yang berhadapan sama panjang dan
        sejajar.
    b. Keempat sudutnya sama besar dan merupakan sudut sikusiku (90⁰).
    c. Kedua diagonalnya sama panjang dan berpotongan membagi dua sama besar.
    d. Dapat menempati bingkainya kembali dengan empat cara.
    e. Mempunyai 2 simetri lipat / sumbu simetri

2. PERSEGI
    Persegi adalah bangun segi empat yang memiliki empat sisi sama panjang
     dan empat  sudut  siku-siku.
     a. Semua sisi persegi adalah sama panjang.
     b. Sudut-sudut suatu persegi dibagi dua sama besar oleh diagonaldiagonalnya.
     c. Diagonal-diagonal persegi saling berpotongan sama panjang membentuk
           sudut siku - siku
     d. Mempunyai 4 sumbu simetri
     e. Menempati bingkainya dengan 8 cara

KELILING DAN LUAS PERSEGI DAN PERSEGI PANJANG

Keliling bangun datar = Jumlah semua sisinya
K persegi = s + s + s + s                            K persegi panjang = p + l + p + l
K persegi = 4s                                           K persegi panjang = 2(p + l)

L ersegi = s x s                                          L persegi panjang = p x l
L persegi = s ²Contoh : Diketahui luas persegi adalah 64 cm ² , tentukan kelilingnya
Diketahui : L = cm ²
Ditanya    : K .... ?
Jawab      : L =  s ²64 cm ² = s ²                                   Jadi K = 4s
√64 cm ²= s                                          K = 4 x 8
                       8 cm = s                                         K = 32 cm

SOAL :
Diketahui persegi dengan luas = 169 cm ² , tentukan keliling persegi tersebut

The given answer is the correct answer because it matches the calculation of the perimeter (keliling) of a square. The formula for the perimeter of a square is K = 4s, where s is the length of one side of the square. In this case, the given length of one side is 52 cm, so when we substitute that value into the formula, we get K = 4(52) = 208 cm. Therefore, the correct answer is K = 52 cm, 52 cm, 52.

Explanation

The given answer is the correct answer because it matches the calculation of the perimeter (keliling) of a square. The formula for the perimeter of a square is K = 4s, where s is the length of one side of the square. In this case, the given length of one side is 52 cm, so when we substitute that value into the formula, we get K = 4(52) = 208 cm. Therefore, the correct answer is K = 52 cm, 52 cm, 52.

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9. CONTOH :
Halaman rumah berbentuk persegi panjang berukuran panjang 90 meter dan lebar 65 meter. Di sekeliling halaman itu, akan dipasang pagar dengan biaya Rp135.000,00 per meter. Berapakah biaya yang diperlukan untuk pemasangan pagar tersebut?

Diketahui : p = 90 m
                  l = 65 m
                  biaya = Rp. 135.000,00 per meter
Ditanya   : biaya pembuatan pagar seluruh halaman
Jawab     : K = 2 ( p + l )
                 K = 2 ( 90 + 65 )
                 K = 2 ( 155 )
                 K = 310 m
Jadi harga pembuatan pagar halaman adalah
310 m x Rp. 135.000 = Rp. 41.850.000,00

SOAL :
Halaman rumah berbentuk persegi panjang berukuran panjang 70 meter dan lebar 50 meter. Di sekeliling halaman itu, akan dipasang pagar dengan biaya Rp120.000,00 per meter. Berapakah biaya yang diperlukan untuk pemasangan pagar tersebut?

The correct answer is Rp.28.800.000,00. To calculate the cost of installing the fence, we need to find the perimeter of the rectangular yard. The perimeter is calculated by adding the lengths of all the sides. In this case, the length is 70 meters and the width is 50 meters. So the perimeter is 2(70+50) = 2(120) = 240 meters. The cost per meter is given as Rp120.000,00. Therefore, the total cost is 240 meters x Rp120.000,00 = Rp.28.800.000,00.

Explanation

The correct answer is Rp.28.800.000,00. To calculate the cost of installing the fence, we need to find the perimeter of the rectangular yard. The perimeter is calculated by adding the lengths of all the sides. In this case, the length is 70 meters and the width is 50 meters. So the perimeter is 2(70+50) = 2(120) = 240 meters. The cost per meter is given as Rp120.000,00. Therefore, the total cost is 240 meters x Rp120.000,00 = Rp.28.800.000,00.

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