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算出 X 的面积 = kira luas X 先数底：X 的底从一条格线到另一条格线，共六格，所以底是六单位。再数高：从顶点笔直往下画虚线到底边，共五格，所以高是五单位。代入公式：二分之一乘六乘五，等于十五平方单位。 例子：底 8 单位、高 3 单位的三角形，面积 = ½ × 8 × 3 = 12 unit²。 注意：高要沿着格线竖直地数，不能沿着斜边数。

the area of X = kira luas X Count the base first: the base of X spans six squares, so it is 6 units. Then the height: draw a dashed line straight down from the top corner to the base; it spans five squares, so the height is 5 units. ½ × 6 × 5 = 15 square units. Example: a triangle with base 8 units and height 3 units has an area of ½ × 8 × 3 = 12 unit². Watch out: count the height straight down along a grid line, not along a slanting side.

高在外面 = tinggi di luar segi tiga Y 的顶点在底边的右边外面，所以要把底边用虚线延长，再从顶点竖直往下画到延长线上。高仍然是五格，底仍然是六格，面积也是二分之一乘六乘五，等于十五平方单位。两个三角形面积相同，这样就证明了。 例子：底 4 单位、顶点在外面、高 7 单位的三角形，面积 = ½ × 4 × 7 = 14 unit²。 注意：延长出来的那一段虚线不算在底里面。

height outside = tinggi di luar segi tiga The top corner of Y lies to the right of its base, so extend the base with a dashed line and drop the height straight down onto it. The height is still five squares and the base still six, so the area is ½ × 6 × 5 = 15 square units as well. The two areas are equal, and that is the proof. Example: a triangle with base 4 units and its top corner outside, height 7 units, has an area of ½ × 4 × 7 = 14 unit². Watch out: the extended dashed part is not part of the base.

用长方形证明 = bukti dengan segi empat tepat 在 X 外面画一个刚好包住它的长方形：长六格、宽五格，面积三十平方单位。高把长方形分成左右两块，每一块都被 X 的斜边对半切开，X 占了每一块的一半。所以 X 的面积是长方形的一半，三十的一半是十五平方单位，和第一种方法结果一样。 例子：包住某个三角形的长方形是 4 × 6 = 24 unit²，那个三角形就是 12 unit²。 注意：长方形的长和宽要和三角形的底和高一样。

proof with a rectangle = bukti dengan segi empat tepat Draw the rectangle that just fits around X: six squares long and five squares wide, 30 square units. The height splits it into a left and a right part, and the slanting sides of X cut each part exactly in half. So X is half of the rectangle: half of 30 is 15 square units, the same result as the first method. Example: if the rectangle around a triangle is 4 × 6 = 24 unit², the triangle is 12 unit². Watch out: the rectangle's length and width must match the triangle's base and height.

顶点沿平行线移动 = bucu bergerak pada garis selari 把 X 和 Y 放在同一条底上：两个顶点都在红色的线上，这条红线和底平行。平行线之间的距离处处相等，所以不管顶点移到红线上的哪里，高都是五格。底一样、高一样，面积就一样。 例子：底都是 3 单位、顶点都在离底 4 单位的平行线上，两个三角形面积都是 6 unit²。 注意：形状变瘦变斜，面积不一定变；要看底和高。

moving the top corner along a parallel line = bucu bergerak pada garis selari Put X and Y on the same base: both top corners lie on the red line, which is parallel to the base. Parallel lines stay the same distance apart, so wherever the corner moves along the red line, the height stays five squares. Same base, same height, same area. Example: two triangles on a 3-unit base with their top corners on a parallel line 4 units away both have an area of 6 unit². Watch out: a thinner or more slanted shape does not always change the area; check the base and height.

比较两个三角形 = banding dua segi tiga 一个三角形又高又窄，另一个又矮又宽，不能凭感觉判断。先数每个三角形的底有几格，再数从顶点竖直到底边有几格，分别代入二分之一乘底乘高，最后比较两个结果。 例子：底 4、高 6 的三角形是 12 unit²，底 5、高 4 的三角形是 10 unit²，两个面积不相等。 注意：高一定要竖直地数到底边那一行。

comparing two triangles = banding dua segi tiga One triangle is tall and narrow, the other short and wide, so do not judge by feeling. Count the squares in each base, then the squares straight down from the top corner to the base, use ½ × base × height for each, and compare the two results. Example: a triangle with base 4 and height 6 has 12 unit², while one with base 5 and height 4 has 10 unit², so these two are not equal. Watch out: always count the height straight down to the row of the base.

找出面积不同的 = cari luas yang berbeza 四个三角形里有三个面积相同。逐一数出每个三角形的底和高，算出面积，写在旁边，再看哪一个和其他三个不一样。直角三角形的两条直角边就是底和高。 例子：底 3、高 8 的三角形面积是 12 unit²，底 6、高 4 的也是 12 unit²。 注意：最扁或最高的那个不一定就是不同的那个，要算过才知道。

find the different area = cari luas yang berbeza Three of the four triangles have the same area. Count the base and height of each one, work out the area, write it beside the triangle, and see which one does not match the other three. In a right-angled triangle the two sides at the right angle are the base and height. Example: a triangle with base 3 and height 8 has 12 unit², and so does one with base 6 and height 4. Watch out: the flattest or tallest triangle is not always the different one; you have to calculate.

三角形和长方形比较 = segi tiga dan segi empat tepat 三角形的面积是底乘高的一半，长方形的面积是长乘宽。分别用各自的公式算出两个面积，写上单位，再比较大小。 例子：底 6 cm、高 4 cm 的三角形是 12 cm²，4 cm × 4 cm 的正方形是 16 cm²，正方形比较大。 注意：三角形一定要乘二分之一。

triangle and rectangle = segi tiga dan segi empat tepat A triangle's area is half of base × height; a rectangle's area is length × width. Work out each area with its own formula, write the units, then compare. Example: a triangle with base 6 cm and height 4 cm is 12 cm², while a 4 cm × 4 cm square is 16 cm², so the square is bigger. Watch out: always multiply the triangle by ½.