Unit 11
Selesaikan Masalah
Masalah perimeter, luas dan isi padu diselesaikan dengan empat langkah:
① Fahami soalan ② Fikir cara ③ Selesaikan ④ Semak
Lukis gambar rajah untuk membantu.
解决空间问题 = selesaikan masalah ruang
周长、面积、体积的应用题都用四个步骤：先读懂题目，列出已知的长度和要找的东西；再想办法，最好画一个简单的图，决定是求周长、面积还是体积；然后计算，写上正确的单位；最后用相反的运算或另一种方法检查。
例子：花圃每边 5 m，围篱笆要 5 × 4 = 20 m，铺草要 5 × 5 = 25 m²。
注意：围一圈是周长（m），铺满是面积（m²），装满是体积（m³）。
solving space problems = selesaikan masalah ruang
Perimeter, area and volume word problems use the same four steps: understand the question and list the lengths given and what is asked; plan, ideally with a quick sketch, deciding whether you need perimeter, area or volume; calculate with the right unit; and check with the opposite operation or another method.
Example: a flower bed with 5 m sides needs 5 × 4 = 20 m of fencing and 5 × 5 = 25 m² of grass.
Watch out: going around is perimeter (m), covering is area (m²) and filling is volume (m³).
Perimeter dan luas
Gelanggang silat
Gelanggang silat berbentuk segi empat sama. Sisinya 11 m. (a) Berapakah panjang pita di sekeliling gelanggang? (b) Berapakah luas gelanggang?
Fahami soalan
• segi empat sama, sisi 11 m
• (a) sekeliling → perimeter
• (b) luas
• (a) sekeliling → perimeter
• (b) luas
Fikir cara
Lukis rajah: 4 sisi sama panjang.
(a) 4 × sisi
(b) sisi × sisi
(a) 4 × sisi
(b) sisi × sisi
Selesaikan
(a) 11 m + 11 m + 11 m + 11 m = 44 m
(b) 11 m × 11 m = 121 m²
(b) 11 m × 11 m = 121 m²
Semak
44 m ÷ 4 = 11 m ✔
121 m² ÷ 11 m = 11 m ✔
121 m² ÷ 11 m = 11 m ✔
周长和面积 = perimeter dan luas
先画一个正方形，四条边都写上十一米。“绕一圈的彩带”是周长：四条边相加，或者用四乘十一，得四十四米。“场地有多大”是面积：边长乘边长，十一乘十一得一百二十一平方米。检查：周长除以四回到边长，面积除以边长也回到边长。
例子：每边 7 m 的正方形场地，周长 28 m，面积 49 m²。
注意：周长用 m，面积用 m²，两个答案的单位不一样。
perimeter and area = perimeter dan luas
Sketch a square and write 11 m on every side. The ribbon around it is the perimeter: add the four sides, or 4 × 11 = 44 m. How big the floor is means area: side × side, 11 × 11 = 121 m². Check: the perimeter ÷ 4 gives back the side, and the area ÷ the side gives back the side.
Example: a square court with 7 m sides has a perimeter of 28 m and an area of 49 m².
Watch out: perimeter is in m and area in m², so the two answers have different units.
Perimeter sama, luas berbeza
Pagar kebun sayur
Encik Daud ada 40 m dawai untuk memagar kebun sayur. Reka bentuk A: segi empat sama bersisi 10 m. Reka bentuk B: segi empat tepat 14 m × 6 m. Reka bentuk manakah memberi kebun yang lebih luas?
Fahami soalan
• dawai 40 m
• A: 10 m × 10 m
• B: 14 m × 6 m
• banding luas
• A: 10 m × 10 m
• B: 14 m × 6 m
• banding luas
Fikir cara
Semak perimeter kedua-duanya 40 m,
kemudian kira dan banding luas.
kemudian kira dan banding luas.
Selesaikan
Perimeter A = 4 × 10 m = 40 m
Perimeter B = 2 × (14 m + 6 m) = 40 m
Luas A = 100 m² · Luas B = 84 m²
Perimeter B = 2 × (14 m + 6 m) = 40 m
Luas A = 100 m² · Luas B = 84 m²
Semak
100 m² − 84 m² = 16 m²
A lebih luas sebanyak 16 m² ✔
A lebih luas sebanyak 16 m² ✔
周长相同面积不同 = perimeter sama, luas berbeza
两种设计都刚好用完四十米铁丝：A 是四乘十，B 是二乘十四加六，都是四十米。可是面积不一样：A 十乘十等于一百平方米，B 十四乘六等于八十四平方米。所以 A 种的菜地比较大，多十六平方米。
例子：周长都是 24 m，6 m × 6 m 的面积 36 m²，10 m × 2 m 的只有 20 m²。
注意：周长一样，面积不一定一样；越接近正方形，面积越大。
same perimeter, different area = perimeter sama, luas berbeza
Both designs use exactly 40 m of wire: A is 4 × 10 and B is 2 × (14 + 6), both 40 m. But the areas differ: A is 10 × 10 = 100 m² and B is 14 × 6 = 84 m². So design A gives the bigger plot, by 16 m².
Example: with a 24 m perimeter, 6 m × 6 m gives 36 m² but 10 m × 2 m gives only 20 m².
Watch out: the same perimeter does not mean the same area; the closer to a square, the bigger the area.
Isi padu
Kiub mainan di dalam kotak
Aina mengisi sebuah kotak berukuran 25 cm × 10 cm × 10 cm dengan kiub mainan bersisi 5 cm sehingga penuh. Berapa banyak kiub mainan yang muat?
Fahami soalan
• kotak: 25 cm × 10 cm × 10 cm
• kiub: sisi 5 cm
• berapa kiub muat?
• kiub: sisi 5 cm
• berapa kiub muat?
Fikir cara
isi padu kotak ÷ isi padu sebuah kiub
Selesaikan
Kotak: 25 × 10 × 10 = 2 500 cm³
Kiub: 5 × 5 × 5 = 125 cm³
2 500 ÷ 125 = 20 buah
Kiub: 5 × 5 × 5 = 125 cm³
2 500 ÷ 125 = 20 buah
Semak
Ikut sisi: 25 ÷ 5 = 5, 10 ÷ 5 = 2, 10 ÷ 5 = 2
5 × 2 × 2 = 20 ✔
5 × 2 × 2 = 20 ✔
装小正方体 = muatkan kiub
要知道盒子装得下几个小正方体，先求盒子的体积：二十五乘十乘十，等于二千五百立方厘米；再求一个小正方体的体积：五乘五乘五，等于一百二十五立方厘米；用大的除以小的，得二十个。检查：长边能放五个，宽和高各放两个，五乘二乘二也是二十。
例子：30 cm × 10 cm × 10 cm 的盒子装边长 10 cm 的方块：3 × 1 × 1 = 3 个。
注意：盒子的边长要刚好是小正方体边长的倍数，才能这样算。
fitting cubes = muatkan kiub
To find how many cubes fit, find the box's volume: 25 × 10 × 10 = 2 500 cm³; then one cube: 5 × 5 × 5 = 125 cm³; divide the big by the small to get 20. Check: five cubes fit along the long edge and two along each of the others, and 5 × 2 × 2 = 20 too.
Example: a 30 cm × 10 cm × 10 cm box holds 3 × 1 × 1 = 3 blocks with 10 cm sides.
Watch out: this works when each box edge is a multiple of the cube's edge.
Cuba
Sebuah papan tanda berukuran 6 m × 4 m. Ayah memasang jalur lampu di sekeliling tepinya. Berapakah panjang jalur lampu yang diperlukan?
绕边一圈 = di sekeliling tepi
灯带要绕着招牌四周装一圈，所以要找的是周长，不是面积。长方形有两条长边和两条宽边，把四条边都加起来，或者用二乘长加宽。
例子：一块 5 m × 2 m 的看板，四周贴一圈胶带要 5 + 2 + 5 + 2 = 14 m。
注意：只加一条长和一条宽是半圈；长乘宽是铺满的面积。
around the edge = di sekeliling tepi
The light strip goes all around the signboard, so you need the perimeter, not the area. A rectangle has two long sides and two short sides; add all four, or do 2 × (length + width).
Example: taping around a 5 m × 2 m notice board needs 5 + 2 + 5 + 2 = 14 m of tape.
Watch out: one length plus one width is only half the way round, and length × width is the area.
Cuba
Sebuah laci berukuran 30 cm × 12 cm × 6 cm diisi penuh dengan kotak kecil berbentuk kubus bersisi 6 cm. Berapakah bilangan kotak kecil itu?
抽屉装方盒 = laci diisi kotak kubus
先算抽屉的体积（长乘宽乘高），再算一个小方盒的体积（边长连乘三次），用抽屉的体积除以小盒的体积。也可以看每条边各放得下几个，再相乘，用来检查。
例子：20 cm × 10 cm × 5 cm 的盒子装边长 5 cm 的方块：1 000 ÷ 125 = 8 个。
注意：要除以小方盒的体积，不是只除以它的边长或一个面的面积。
a drawer of cube boxes = laci diisi kotak kubus
Find the drawer's volume (length × width × height), then one small box's volume (the side three times), and divide the drawer's volume by the small box's volume. You can check by finding how many fit along each edge and multiplying.
Example: a 20 cm × 10 cm × 5 cm box holds 1 000 ÷ 125 = 8 blocks with 5 cm sides.
Watch out: divide by the small box's volume, not just by its edge or the area of one face.
Cuba
Sebuah kotak diisi penuh dengan 40 biji kiub bersisi 2 cm. Berapakah isi padu kotak itu?
个数乘小方块体积 = bilangan kiub × isi padu sebuah kiub
盒子被小正方体装满，盒子的体积就等于所有小正方体体积的总和。先算一个小正方体的体积（边长连乘三次），再乘小正方体的个数。
例子：12 个边长 4 cm 的方块装满一个盒子：一个 64 cm³，盒子 = 12 × 64 = 768 cm³。
注意：小正方体的个数不是体积，还要乘每个的体积。
number of cubes × volume of one cube = bilangan kiub × isi padu sebuah kiub
When a box is completely filled with small cubes, its volume equals the total volume of all the cubes. Find one cube's volume (the side three times), then multiply by the number of cubes.
Example: 12 blocks with 4 cm sides fill a box; one block is 64 cm³, so the box is 12 × 64 = 768 cm³.
Watch out: the number of cubes is not the volume; multiply by each cube's volume.
Ringkasan
Syabas!
4 langkah
Fahami soalan, lukis rajah, pilih perimeter, luas atau isi padu, kira dengan unit yang betul dan semak.
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