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Unit 7 · Luas
Unit 7

Luas

Kelas 4 Bestari mahu menutup papan kenyataan dengan kertas petak yang sama saiz. Berapa keping kertas petak diperlukan?
Bilangan petak itu ialah luas papan kenyataan.

Luas
面积 = luas 面积是一个平面图形表面的大小。把图形铺满一样大的小正方形，数一数用了多少个，就知道面积。边长一单位的小正方形叫做一平方单位。以后还会学用乘法很快算出长方形、正方形和三角形的面积。 例子：一块板铺了 3 行，每行 5 张方形纸，面积就是 15 平方单位。 注意：面积看的是里面铺满多少，不是绕边走一圈有多长。
area = luas Area is the size of the flat surface inside a shape. Cover the shape with equal small squares and count them. A square with sides of one unit is called one square unit. Soon you will also use multiplication to find the area of rectangles, squares and triangles quickly. Example: a board covered by 3 rows of 5 square papers has an area of 15 square units. Watch out: area is how much space is covered inside, not the distance around the edge.
Unit persegi

Kira petak

1 petak = 1 unit persegi (1 unit²)

Luas = 10 unit persegi = 10 unit²
平方单位 = unit persegi 边长一单位的小正方形，面积是一平方单位，写作 1 unit²。数一数图形里铺了多少个这样的小方格，就是它的面积。这里绿色图形一行五格、共两行，一共十格，所以面积是十平方单位。 例子：一个图形铺满 8 个小方格，面积是 8 unit²。 注意：要数的是格子的个数，不是格线的条数。
square unit = unit persegi A small square with sides of one unit has an area of one square unit, written 1 unit². Count how many of these squares cover the shape and you have its area. The green shape has two rows of five squares, ten squares in all, so its area is ten square units. Example: a shape covered by 8 small squares has an area of 8 unit². Watch out: count the squares, not the grid lines.
Baris dan lajur

Panjang × lebar

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unit × 3 unit = 21 unit²
长乘宽 = panjang × lebar 长方形里的格子排得很整齐：每一行的格数就是长，有几行就是宽。所以不用一格一格数，只要用长乘宽：七乘三等于二十一，和七加七加七的结果一样，面积是二十一平方单位。 例子：长 6 单位、宽 4 单位的长方形，面积 = 6 × 4 = 24 平方单位。 注意：乘法只适用于铺得整整齐齐的长方形和正方形。
length × width = panjang × lebar The squares in a rectangle sit in neat rows: the squares in one row give the length, and the number of rows gives the width. So instead of counting one by one, multiply length by width: 7 × 3 = 21, the same as 7 + 7 + 7, so the area is 21 square units. Example: a rectangle 6 units long and 4 units wide has an area of 6 × 4 = 24 square units. Watch out: this multiplication works for neat rectangles and squares.
Luas dalam cm²

Kad ucapan

Luas = panjang × lebar

8 cm5 cm
Luas = 8 cm × 5 cm = 40 cm²

cm × cm = cm² (sentimeter persegi)

平方厘米 = sentimeter persegi 边长一厘米的正方形，面积是一平方厘米，写作 cm²。长方形的长和宽都用厘米量时，面积 = 长 × 宽，单位从 cm 变成 cm²，因为厘米乘厘米得平方厘米。这张卡长八厘米、宽五厘米，面积是四十平方厘米。 例子：书签长 11 cm、宽 3 cm，面积 = 33 cm²。 注意：只写 cm 是长度的单位，面积一定要写 cm²。
square centimetre = sentimeter persegi A square with 1 cm sides has an area of one square centimetre, written cm². When length and width are both in centimetres, area = length × width and the unit becomes cm², because cm × cm = cm². This card is 8 cm by 5 cm, so its area is 40 cm². Example: a bookmark 11 cm long and 3 cm wide has an area of 33 cm². Watch out: cm alone is a unit of length; area must be written in cm².
Luas dalam m²

Lantai pentas

Segi empat sama: sisi × sisi

7 m7 m
Luas = 7 m × 7 m = 49 m²

Kawasan besar (lantai, padang) → m² · objek kecil (buku, kad) → cm²

平方米 = meter persegi 正方形四条边一样长，所以面积 = 边长 × 边长。舞台地板每边七米，面积 = 七米乘七米，等于四十九平方米。米乘米得平方米 m²。量地板、球场、墙壁这些大地方用平方米，量书本、卡片这些小东西用平方厘米。 例子：每边 10 m 的花园，面积 = 100 m²。 注意：选单位时先想想东西有多大，教室地板不会用 cm² 来量。
square metre = meter persegi All four sides of a square are equal, so area = side × side. The stage floor has 7 m sides, so its area is 7 m × 7 m = 49 m². Metres times metres give square metres, m². Big places such as floors, fields and walls are measured in m²; small things such as books and cards in cm². Example: a garden with 10 m sides has an area of 100 m². Watch out: think about the size of the object when choosing the unit; a classroom floor is not measured in cm².
Segi tiga

Separuh segi empat tepat

10 cm6 cm½ × 10 cm × 6 cm = 30 cm²
三角形面积 = luas segi tiga 沿对角线把长方形剪开，会得到两个一样大的三角形，所以三角形的面积是长方形的一半。方法一：先算长方形十乘六得六十平方厘米，再除以二得三十。方法二：用公式二分之一乘底乘高，二分之一乘十乘六也是三十平方厘米。 例子：底 8 cm、高 5 cm 的三角形，面积 = ½ × 8 × 5 = 20 cm²。 注意：千万别忘了二分之一，否则算出来的是整个长方形。
area of a triangle = luas segi tiga Cutting a rectangle along its diagonal gives two equal triangles, so a triangle's area is half of the rectangle. Way 1: the rectangle is 10 × 6 = 60 cm², and half of that is 30 cm². Way 2: use ½ × base × height: ½ × 10 × 6 = 30 cm² as well. Example: a triangle with base 8 cm and height 5 cm has an area of ½ × 8 × 5 = 20 cm². Watch out: never forget the ½, or you get the whole rectangle.
Tapak dan tinggi

Tinggi berserenjang dengan tapak

tapaktinggitapaktinggitapaktinggi

Garis jingga putus-putus = tinggi. Tanda merah = sudut tegak.

底和高 = tapak dan tinggi 三角形的底一般是下面那条边；高是从顶点垂直落到底边（或底边的延长线）的距离，和底成直角。直角三角形的高就是那条竖直的直角边；斜斜的三角形，高要另外画出来，有时候还会落在三角形外面。 例子：直角三角形两条直角边是 9 cm 和 4 cm，一条当底，另一条就是高。 注意：斜边不是高，因为斜边和底没有成直角。
base and height = tapak dan tinggi The base of a triangle is usually the bottom side. The height is the straight-up distance from the top corner to the base (or to the base extended), and it makes a right angle with the base. In a right-angled triangle the height is the upright side; in a slanted triangle the height has to be drawn, and it may even fall outside the triangle. Example: in a right-angled triangle with sides 9 cm and 4 cm around the right angle, one is the base and the other is the height. Watch out: a slanting side is not the height, because it does not meet the base at a right angle.
Pilih tinggi

Kad manakah betul?

14 cm8 cm10 cm

Kad A ✗

½ × 14 cm × 10 cm
= 70 cm²

Kad B ✓

½ × 14 cm × 8 cm
= 56 cm²
选对高 = pilih tinggi yang betul 图上有三个数字：底十四厘米、斜边十厘米、虚线八厘米。虚线和底成直角，才是高；十厘米那条边是斜的，不是高。所以 B 卡用二分之一乘十四乘八，得五十六平方厘米，是对的；A 卡用了斜边，算错了。 例子：底 10 cm、斜边 7 cm、高 6 cm，面积 = ½ × 10 × 6 = 30 cm²。 注意：找高时先找直角记号。
choose the right height = pilih tinggi yang betul The picture shows three numbers: base 14 cm, slanting side 10 cm and the dashed line 8 cm. Only the dashed line meets the base at a right angle, so it is the height; the 10 cm side is slanted. Card B uses ½ × 14 × 8 = 56 cm² and is correct; Card A used the slanting side. Example: base 10 cm, slanting side 7 cm, height 6 cm gives ½ × 10 × 6 = 30 cm². Watch out: look for the right-angle mark to find the height.
Semak cepat

Berapakah luas segi empat tepat ini?

12 cm5 cm
长方形的面积 = luas segi empat tepat 长方形的面积用长乘宽来算，单位是平方厘米。先在图上找出长和宽各是多少，再相乘，最后写上带小小的 2 的单位。 例子：一张贴纸长 9 cm、宽 2 cm，面积 = 9 cm × 2 cm = 18 cm²。 注意：把四条边加起来得到的是周长，不是面积；只把长和宽相加也不对。
area of a rectangle = luas segi empat tepat The area of a rectangle is length × width, in square centimetres. Find the length and the width in the picture, multiply them, and write a unit with the small 2. Example: a sticker 9 cm long and 2 cm wide has an area of 9 cm × 2 cm = 18 cm². Watch out: adding all four sides gives the perimeter, not the area, and adding only the length and width is not right either.
Semak cepat

Berapakah luas segi tiga ini?

22 cm15 cm17 cm
三角形面积公式 = ½ × tapak × tinggi 先找底，再找和底成直角的那条虚线当作高，不要用斜边。把底和高相乘，再取一半，单位是平方厘米。 例子：底 12 cm、斜边 10 cm、高 8 cm 的三角形，面积 = ½ × 12 × 8 = 48 cm²。 注意：只乘底和高、没有除以二，得到的是长方形的面积。
triangle formula = ½ × tapak × tinggi Find the base, then the dashed line that meets the base at a right angle; that is the height, not the slanting side. Multiply the base by the height and take half, in square centimetres. Example: a triangle with base 12 cm, slanting side 10 cm and height 8 cm has an area of ½ × 12 × 8 = 48 cm². Watch out: multiplying the base by the height without halving gives a rectangle's area.
Semak cepat

Luas sebuah segi empat tepat ialah 56 cm². Panjangnya 8 cm. Berapakah lebarnya?

已知面积求宽 = cari lebar 长方形的面积 = 长 × 宽。现在知道面积和长，要找宽，就想：长乘几等于面积？用除法：面积 ÷ 长 = 宽。宽是一段长度，单位写 cm。 例子：面积 45 cm²、长 9 cm，宽 = 45 ÷ 9 = 5 cm。 注意：面积减去长，或面积加上长，都不是求宽的方法。
finding the width = cari lebar Area of a rectangle = length × width. You know the area and the length, so ask: the length times what number gives the area? Divide: area ÷ length = width. The width is a length, so its unit is cm. Example: area 45 cm² and length 9 cm give a width of 45 ÷ 9 = 5 cm. Watch out: subtracting the length from the area, or adding them, does not give the width.
Pilih saiz

Dinding bilik Mira setinggi 2 m. Gulungan kertas dinding ada dua saiz: 150 cm dan 250 cm panjang. Saiz manakah dapat menutup dinding dari lantai hingga siling dengan sehelai?

选合适的尺寸 = pilih saiz yang sesuai 墙高用米表示，墙纸长度用厘米表示，单位不同不能直接比较。先把米换成厘米（1 m = 100 cm），再看哪一种墙纸的长度够从地板贴到天花板，不够长的就会留下一段空白。 例子：窗高 1 m，要遮住整扇窗，80 cm 的布太短，120 cm 的布够长。 注意：比较长度前，一定要先把单位换成一样。
choosing a suitable size = pilih saiz yang sesuai The wall height is in metres and the wallpaper lengths are in centimetres, so they cannot be compared directly. Change metres to centimetres first (1 m = 100 cm), then see which roll is long enough to reach from floor to ceiling; a roll that is too short leaves a gap. Example: to cover a window 1 m high, an 80 cm curtain is too short but a 120 cm one is long enough. Watch out: always change to the same unit before comparing lengths.
Ringkasan

Syabas!

cm² · m² · ½ × tapak × tinggi

Luas segi empat = panjang × lebar. Luas segi tiga = ½ × tapak × tinggi; tinggi berserenjang dengan tapak.

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