Unit 6
Akal Pintar
Cikgu Lina memberi setiap kumpulan seutas dawai 24 cm. Setiap kumpulan mesti membengkokkan seluruh dawai itu menjadi sebuah poligon sekata, dan panjang setiap sisi mesti nombor bulat. Poligon sekata apakah yang boleh dibentuk?
从周长找正多边形 = cari poligon sekata daripada perimeter
整条铁线都用来围成图形，所以铁线的长度就是图形的周长。正多边形每条边一样长，周长等于边数乘边长。反过来想：周长除以边长，就得到边数；知道边数，就知道是哪一种正多边形。
例子：一条 12 cm 的铁线围成每边 4 cm 的正多边形，12 ÷ 4 = 3，是正三角形。
注意：边长要是整数，所以周长要能被边数整除。
finding a regular polygon from its perimeter = cari poligon sekata daripada perimeter
The whole wire is used, so the wire's length is the shape's perimeter. A regular polygon has equal sides, so perimeter = number of sides × side length. Working backwards, perimeter ÷ side length gives the number of sides, which tells us which regular polygon it is.
Example: a 12 cm wire bent into a regular polygon with 4 cm sides gives 12 ÷ 4 = 3 sides, an equilateral triangle.
Watch out: the side must be a whole number, so the perimeter must divide exactly by the number of sides.
Cara
Bilangan sisi = perimeter ÷ panjang sisi
Perimeter 24 cm, sisi 6 cm
24 ÷ 6 = 4 → 4 sisi → segi empat sama
用除法找边数 = bahagi untuk cari bilangan sisi
周长二十四厘米，每边六厘米。问“二十四里面有几个六”，就是二十四除以六，等于四。有四条一样长的边、四个直角的正多边形，就是正方形。最后用乘法检查：四乘六等于二十四。
例子：周长 54 cm、每边 9 cm：54 ÷ 9 = 6，是正六边形。
注意：除出来的是边数，不是长度，所以没有单位 cm。
dividing to find the number of sides = bahagi untuk cari bilangan sisi
The perimeter is 24 cm and each side is 6 cm. Asking how many sixes are in twenty-four means 24 ÷ 6 = 4. A regular polygon with four equal sides and four right angles is a square. Check by multiplying: 4 × 6 = 24.
Example: perimeter 54 cm with 9 cm sides: 54 ÷ 9 = 6, a regular hexagon.
Watch out: the answer of the division is a number of sides, not a length, so it has no cm.
Lebih daripada satu jawapan
Dawai 24 cm
Panjang sisi mesti nombor bulat
| Poligon sekata | Sisi | Panjang sisi |
|---|---|---|
| segi tiga sama sisi | 3 | 24 ÷ 3 = 8 cm |
| segi empat sama | 4 | 24 ÷ 4 = 6 cm |
| heksagon sekata | 6 | 24 ÷ 6 = 4 cm |
| oktagon sekata | 8 | 24 ÷ 8 = 3 cm |
| pentagon sekata | 5 | 24 ÷ 5 ✗ |
同一条铁线，多种答案 = satu dawai, banyak jawapan
用边数去除周长：能整除，边长就是整数，这种正多边形就可以围成。二十四能被三、四、六、八整除，所以正三角形、正方形、正六边形、正八边形都可以；二十四除以五除不尽，所以正五边形不行。
例子：一条 30 cm 的铁线可以围成每边 6 cm 的正五边形，因为 30 ÷ 5 = 6。
注意：题目说“哪一种”时，答案可能不止一个。
one wire, many answers = satu dawai, banyak jawapan
Divide the perimeter by the number of sides: if it divides exactly, the side is a whole number and that regular polygon can be made. Twenty-four divides exactly by three, four, six and eight, so a triangle, square, hexagon and octagon all work; it does not divide exactly by five, so a pentagon does not.
Example: a 30 cm wire can make a regular pentagon with 6 cm sides, because 30 ÷ 5 = 6.
Watch out: when a question asks which polygon, there may be more than one answer.
Cuba
Perimeter sebuah poligon sekata ialah 35 cm. Setiap sisi 7 cm. Apakah poligon itu?
判断是哪种正多边形 = kenal pasti poligon sekata
先用周长除以一条边的长度，求出有几条边。再把边数换成名称：三条边、四条边、五条边、六条边……各有自己的名字。最后用边数乘边长，看看是不是等于题目给的周长。
例子：周长 27 cm、每边 9 cm，27 ÷ 9 = 3，是三条边的正多边形。
注意：不要用周长减边长。
which regular polygon = kenal pasti poligon sekata
First divide the perimeter by the length of one side to find how many sides there are. Then turn the number of sides into a name: three, four, five, six sides and so on each have their own name. Finally multiply the number of sides by the side length to check it equals the given perimeter.
Example: perimeter 27 cm with 9 cm sides: 27 ÷ 9 = 3, a three-sided regular polygon.
Watch out: do not subtract the side length from the perimeter.
Pilih
Dawai 18 cm dibentuk menjadi poligon sekata. Panjang sisi mesti nombor bulat. Pilih semua yang boleh.
整数边长的正多边形 = poligon sekata bersisi nombor bulat
逐个检查：先想每一个名称有几条边，再用铁线长度除以边数。除得尽、没有余数，边长才是整数，才可以选；有余数的就不行。可能有几个都可以。
例子：一条 16 cm 的铁线：16 ÷ 4 = 4，可以围成每边 4 cm 的正方形；16 ÷ 3 有余数，不能围成整数边长的正三角形。
注意：每个名称都要算一次。
regular polygons with whole-number sides = poligon sekata bersisi nombor bulat
Check each one: think how many sides the name means, then divide the wire length by that number. Only if it divides exactly, with no remainder, is the side a whole number, so it can be chosen; with a remainder it cannot. Several may work.
Example: with a 16 cm wire, 16 ÷ 4 = 4, so a square with 4 cm sides works; 16 ÷ 3 leaves a remainder, so a triangle with whole-number sides does not.
Watch out: work out every name before pressing Semak.
Cuba
Perimeter oktagon sekata ialah 40 cm. Berapakah panjang setiap sisi?
已知周长求边长 = cari panjang sisi
正多边形的周长平均分给每一条边。所以边长等于周长除以边数。先想八边形有几条边，再把周长平均分成那么多份。最后用乘法检查。
例子：正六边形周长 42 cm，每边 42 ÷ 6 = 7 cm。
注意：边长是一段长度，要带单位。
finding the side from the perimeter = cari panjang sisi
The perimeter of a regular polygon is shared equally among its sides, so side length = perimeter ÷ number of sides. Think how many sides an octagon has, share the perimeter into that many equal parts, then check by multiplying.
Example: a regular hexagon with perimeter 42 cm has sides of 42 ÷ 6 = 7 cm.
Watch out: a side length is a length, so it needs a unit.
Ringkasan
Syabas!
sisi = perimeter ÷ panjang sisi
Bahagikan perimeter dengan panjang sisi untuk mencari bilangan sisi poligon sekata.
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