Unit 1

Kenal Prisma dan Bukan Prisma

Di gerai pesta sekolah ada kotak hadiah, dadu besar dan khemah kecil.
Ketiga-tiga benda ini berbentuk prisma. Mari kenal bentuknya!

kotak

dadu

khemah

棱柱 = prisma；非棱柱 = bukan prisma；立体图形 = bentuk tiga dimensi 这一课认识立体图形里的“棱柱”。学校园游会的摊位上有礼物盒、大骰子和小帐篷，它们的形状都是棱柱：礼物盒是长方体，骰子是正方体，帐篷是三角棱柱。后面还会看到球、圆柱、圆锥和金字塔，它们不是棱柱。例子：家里的纸巾盒、牛奶盒都像长方体，是棱柱。注意：判断是不是棱柱，要看它的面和两个底面，不是看它多大或是什么颜色。

prism = prisma; non-prism = bukan prisma; solid shape = bentuk tiga dimensi This unit is about prisms among solid shapes. At the school fair stall there is a gift box, a big dice and a small tent. All three are prisms: the box is a cuboid, the dice is a cube and the tent is a triangular prism. Later we meet the sphere, cylinder, cone and pyramid, which are not prisms. Example: a tissue box or a milk carton at home is shaped like a cuboid, so it is a prism. Watch out: to decide if a shape is a prism, look at its faces and its two bases, not its size or colour.

Tiga jenis prisma

Nama prisma ikut bentuk tapaknya

Tapak = dua permukaan yang sama dan bertentangan

kubus
prisma segi empat sama

kuboid
prisma segi empat tepat

prisma segi tiga
tapak segi tiga

Warna jingga = tapak (depan dan belakang)

正方体 = kubus；长方体 = kuboid；三角棱柱 = prisma segi tiga 棱柱的名字是看它的底面（tapak）来取的。正方体的底面是正方形，所以又叫 prisma segi empat sama；长方体的底面是长方形，叫 prisma segi empat tepat；三角棱柱的底面是三角形。图里橙色的就是两个底面，一前一后。例子：一块三角形的芝士蛋糕，前后两面都是三角形，所以是三角棱柱。注意：底面一定是一对，形状、大小都一样，而且面对面。

cube = kubus; cuboid = kuboid; triangular prism = prisma segi tiga A prism is named after the shape of its base (tapak). A cube has square bases, so it is also called prisma segi empat sama; a cuboid has rectangular bases, so it is prisma segi empat tepat; a triangular prism has triangle bases. The orange faces in the picture are the two bases, one at the front and one at the back. Example: a wedge of cheesecake has a triangle at the front and at the back, so it is a triangular prism. Watch out: the bases always come as a pair of the same shape and size, facing each other.

Bahagian prisma

Bucu, tepi, permukaan rata

Lihat kuboid ini

● bucu

━ tepi

permukaan rata

Garis putus-putus = tepi yang tersembunyi

顶点 = bucu；棱 = tepi；平面 = permukaan rata 第一个长方体上的红点是顶点，是几条棱碰在一起的尖角；第二个上的红线是棱，是两个面相接的线；第三个整个上色的部分是平面，摸起来是平平的。虚线代表藏在后面、看不到的棱，数的时候也要算进去。例子：骰子的一个尖角是顶点，桌子的边缘线是棱，桌面是平面。注意：看不到的顶点和棱也存在，所以长方体有 8 个顶点，不是只数看得到的 7 个。

vertex = bucu; edge = tepi; flat face = permukaan rata The red dots on the first cuboid are vertices, the corners where edges meet. The red line on the second is an edge, where two faces join. The coloured parts of the third are flat faces that feel smooth and level. The dashed lines are edges hidden at the back, and they still count. Example: a corner of a dice is a vertex, the side line of a table is an edge and the table top is a flat face. Watch out: hidden vertices and edges are still there, so a cuboid has 8 vertices, not just the 7 you can see.

Kira permukaan rata

Kubus: berapa permukaan?

Kira yang nampak dan yang tersembunyi

Kubus: 6 permukaan rata · 12 tepi · 8 bucu

数面 = kira permukaan rata 动画里正方体的面一个个亮起：前、上、右三个看得到，后、左、下三个藏在后面，用红色虚线框表示。全部加起来是 6 个平面。用同样的方法数，正方体有 12 条棱、8 个顶点。数的时候按“前后、上下、左右”成对来数，就不会漏。例子：长方体也一样是 6 个面（前后、上下、左右各一对）。注意：图上只看得到 3 个面，答“3 个面”是常见的错。

counting faces = kira permukaan rata In the animation the faces of the cube light up one by one: front, top and right can be seen, while back, left and bottom are hidden and shown with red dashed outlines. Altogether there are 6 flat faces. Counting the same way, a cube has 12 edges and 8 vertices. Count in pairs, front and back, top and bottom, left and right, so you miss none. Example: a cuboid also has 6 faces, one pair in each direction. Watch out: only 3 faces show in the picture, so answering 3 is a common mistake.

Cuba

Berapakah permukaan rata prisma segi tiga?

三角棱柱的面 = permukaan prisma segi tiga 三角棱柱有前后两个三角形底面，中间绕着一圈长方形的侧面。三角形有 3 条边，所以侧面也有 3 个长方形。2 + 3 = 5，一共 5 个平面。例子：小帐篷前后两个三角形门，加上两边斜屋顶和地面三个长方形，就是 5 个面。注意：只数看得到的面会得到 3；以为跟正方体一样就会答 6。

faces of a triangular prism = permukaan prisma segi tiga A triangular prism has two triangle bases, front and back, with a ring of rectangles around the middle. A triangle has 3 sides, so there are 3 rectangles. 2 + 3 = 5, so there are 5 flat faces in all. Example: a small tent has two triangle doors plus two sloping roof sides and a floor, which is 5 faces. Watch out: counting only the faces you can see gives 3, and thinking it is like a cube gives 6.

Makmal interaktif

Lipat bentangan

Pilih satu bentangan. Tekan Lipat dua kali. Prisma apakah terbentuk?

展开图 = bentangan；折 = lipat；打开 = buka 展开图就是把立体图形剪开、摊平后的样子。选一个展开图，按两次 Lipat，第一次折到一半，第二次折好，就会变回立体。正方体的展开图有 6 个正方形，长方体有 6 个长方形，三角棱柱有 2 个三角形和 3 个长方形。三个都试一次。例子：把一个空牙膏盒沿边剪开摊平，就得到长方体的展开图。注意：展开图有几个面，折好的立体就有几个面。

net = bentangan; fold = lipat; open = buka A net is a solid shape cut open and laid flat. Choose a net and press Lipat twice: the first press folds it halfway and the second finishes the solid. The cube net has 6 squares, the cuboid net has 6 rectangles and the triangular prism net has 2 triangles and 3 rectangles. Try all three nets. Example: cutting an empty toothpaste box along its edges and laying it flat gives a cuboid net. Watch out: the number of faces in the net equals the number of faces of the folded solid.

Semak makmal

Bentangan ada 2 segi tiga dan 3 segi empat tepat. Apabila dilipat, ia menjadi …

看展开图认立体 = kenal bentuk daripada bentangan 两个三角形一前一后，会变成底面；三个长方形绕成一圈，变成侧面。底面是三角形的棱柱就是三角棱柱，正好 5 个面，跟实验台折出来的一样。例子：展开图有 6 个一样的正方形 → 折成正方体。注意：金字塔的侧面是三角形、聚在顶上一个点；长方体没有三角形的面。

naming a solid from its net = kenal bentuk daripada bentangan The two triangles end up at the front and back as the bases, and the three rectangles wrap round to make the sides. A prism with triangle bases is a triangular prism, with exactly 5 faces, just like the one folded in the lab. Example: a net of 6 equal squares folds into a cube. Watch out: a pyramid has triangle sides meeting at one top point, and a cuboid has no triangle faces at all.

Ciri-ciri prisma

Semak tiga ciri

Semua ciri mesti ✓

ciri prisma	kuboid
5 atau lebih permukaan rata	✓ 6
2 tapak sama bentuk dan saiz, berhadapan	✓
tiada permukaan melengkung	✓

Potong selari dengan tapak → keratan sama dengan tapak

棱柱的特征 = ciri-ciri prisma；曲面 = permukaan melengkung 判断棱柱要三项都打勾：一、有 5 个或以上的平面；二、有两个形状大小完全一样、面对面的底面；三、完全没有弯曲的面。长方体三项都符合，所以是棱柱。还有一个好方法：沿着跟底面平行的方向切开，切口永远跟底面一模一样。例子：把一条长方体的面包横着切片，每一片的切面都是同样的长方形。注意：只要有一项打叉，就不是棱柱。

features of a prism = ciri-ciri prisma; curved surface = permukaan melengkung A shape is a prism only when all three boxes are ticked: it has 5 or more flat faces, it has two bases of the same shape and size facing each other, and it has no curved surface. A cuboid passes all three, so it is a prism. Another test: cut it parallel to the base and the cut face always matches the base. Example: slicing a cuboid loaf of bread gives the same rectangle on every slice. Watch out: if even one box gets a cross, the shape is not a prism.

Bukan prisma

Mengapa bukan prisma?

Ada permukaan melengkung, atau tiada dua tapak yang sama

sfera
melengkung

silinder
melengkung

kon
melengkung

piramid
1 tapak sahaja

球体 = sfera；圆柱体 = silinder；圆锥体 = kon；金字塔（棱锥）= piramid 这四个都不是棱柱。球体只有一个弯曲的面；圆柱体虽然上下两个圆一样大，但侧面是弯的；圆锥体也有弯曲的面。金字塔的面都是平的，可是它只有一个底面，侧面的三角形往上聚到一个尖顶，没有第二个底面。例子：篮球是球体，汽水罐是圆柱体，雪糕筒是圆锥体。注意：圆柱体最容易被当成棱柱，记住“有曲面就不是棱柱”。

sphere = sfera; cylinder = silinder; cone = kon; pyramid = piramid None of these four is a prism. A sphere has only one curved surface. A cylinder has two equal circles at the ends, but its side is curved. A cone also has a curved surface. All the faces of a pyramid are flat, but it has only one base, and its triangle sides meet at a single top point, so there is no second base. Example: a basketball is a sphere, a soft drink can is a cylinder and an ice cream cone is a cone. Watch out: the cylinder is the shape most often mistaken for a prism; any curved surface means it is not one.

Cuba

Mengapakah silinder bukan prisma?

圆柱体为什么不是棱柱 = mengapa silinder bukan prisma 圆柱体上下两个圆形一样大，这一点像棱柱；但它的侧面是弯曲的，不符合“没有曲面”这一项，所以不是棱柱。“两个底面不一样大”是错的，它们其实一样大；高不高也跟是不是棱柱无关。例子：摸一摸罐头的侧面，是弯的，所以罐头不是棱柱。注意：理由要说到“曲面”才对。

why a cylinder is not a prism = mengapa silinder bukan prisma The two circles at the ends of a cylinder are the same size, which looks prism-like, but its side surface is curved, so it fails the no-curved-surface test and is not a prism. Saying the bases differ in size is wrong, since they are equal, and height has nothing to do with being a prism. Example: feel the side of a tin can; it bends, so the can is not a prism. Watch out: a correct reason must mention the curved surface.

Cuba

Semua permukaan piramid rata. Adakah piramid sebuah prisma?

金字塔不是棱柱 = piramid bukan prisma 金字塔有 5 个平面，也没有曲面，看起来好像符合两项。但棱柱一定要有两个一样、面对面的底面；金字塔只有底下一个正方形，四个三角形往上聚成一个尖顶，没有第二个底面，所以不是棱柱。例子：三角棱柱前后都是三角形，一前一后面对面；金字塔顶上只是一个点。注意：三项特征要全部符合，只符合两项也不算。

a pyramid is not a prism = piramid bukan prisma A pyramid has 5 flat faces and no curved surface, so it seems to pass two tests. But a prism must have two equal bases facing each other. A pyramid has only the square at the bottom, and its four triangles meet at one top point, so there is no second base and it is not a prism. Example: a triangular prism has a triangle at the front and another at the back; a pyramid has just a point at the top. Watch out: all three features are needed; passing two of them is not enough.

Padankan

Bentuk dan cirinya

配对特征 = padankan ciri 三角棱柱：5 个平面、9 条棱、6 个顶点。正方体：6 个面全部是一样的正方形。金字塔：5 个平面、8 条棱、5 个顶点，跟三角棱柱一样有 5 个面，要靠棱和顶点分辨。圆柱体：上下 2 个圆形平面，加上 1 个弯曲的侧面。例子：长方体也是 6 个面，但不是每个面都是正方形。注意：5 个面的有两种立体，再数一数棱就能分清楚。

matching features = padankan ciri Triangular prism: 5 flat faces, 9 edges, 6 vertices. Cube: 6 faces that are all equal squares. Pyramid: 5 flat faces, 8 edges, 5 vertices; it has 5 faces like the triangular prism, so use the edges and vertices to tell them apart. Cylinder: 2 flat circles plus 1 curved side. Example: a cuboid also has 6 faces, but they are not all squares. Watch out: two different solids have 5 faces, so count the edges to separate them.

Ringkasan

Syabas!

prisma: 2 tapak sama · tiada lengkung

Kubus, kuboid dan prisma segi tiga ialah prisma. Nama prisma ikut tapaknya. Sfera, silinder, kon dan piramid bukan prisma.

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