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本次影片我想講的基本就是

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周長和面積

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左邊寫周長的

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右邊寫面積的

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大家可能對這兩個概念都很熟悉了

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但還是複習一下 以免大家忘了

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周長就是環繞某物一周的長度

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就像你給某個東西裝柵欄

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就像把磁帶環繞某物一周

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量磁帶有多長

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例如

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假設我有一個長方形

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假設有個長方形

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長方形就是

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有4條邊 4個直角的圖形

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這就是一個長方形

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總共有4個直角

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總計有4條邊 而且對邊相等

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因此上下兩邊相等

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左右兩邊也相等

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然後 我把4個頂點標爲A　B C D

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假設已知下列條件

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AB長爲7

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BC長爲7

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那麽這個長方形的周長是多少？

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我先寫下周長

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長方形ABCD的周長就等於

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四邊長度之和

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如果我想建圍欄

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那這就是我的地塊

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我得先知道上邊長多少

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上邊長爲7

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我用紫色標

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上邊長7

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因此就是7加右邊BC

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也就是5

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因爲已知BC爲5

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加上5 再加DC DC與AB等長

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也是7

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因此加7

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最後就是再加DA或AD

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等於BC

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也就是5 因此再加5

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7加5等於12

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7加5等於12

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因此就能算出周長

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因此周長是24

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也可以

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假設有一個正方形

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也就是特殊的長方形

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正方形是有4條邊和4個直角的長方形

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並且4條邊等長

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我畫一個正方形

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我畫一個正方形

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我盡力畫整齊了

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這就是A B C D點

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要記住

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這是一個正方形

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假設已知這個正方形的周長

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周長爲36

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求正方形邊長

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四邊長都相等

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設邊長爲x

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如果AB長x BC長也爲x

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DC與AD長也爲x

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四邊長都相等

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四邊長都相等

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四邊長都相等

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我們稱之爲x

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因此若想求此正方形周長

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那就是4個x相加

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咱們寫下來

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即4x

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也就是36

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這個條件是已知的

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我們需要解決的是

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4乘多少等於36

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你可以心算出結果

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但是兩邊都除以4

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那麽就得出x等於9

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x等於9

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因此這是個邊長爲9的正方形

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這是9 寬是9 高也是9

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以上就是周長的內容

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面積是某物在二維空間中所占的空間

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大家可以這樣理解面積

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就是假設有一個長爲1的正方形

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這個就是長爲1的正方形

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當我說長爲1的正方形時

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對於正方形 長方形只需要確定兩個量就可以

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因爲另外兩個量相等

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比如

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你可以叫這個長方形爲長7寬5長方形

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因爲這就暗示

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如果這個邊長5 那麽這個邊也是5

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這個邊是7的話 這個邊也是7

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就正方形而言 你可以稱邊長爲1的正方形

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這就確定了所有邊長

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這對所有正方形都成立

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如果正方形一條邊是1

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那麽所有的邊都是1

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這就是邊長爲1的正方形

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你可以把面積看作是

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這個空間可以放多少個邊長爲1的正方形

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例如

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回到剛才那個長方形

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我想求那個長方形的面積

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面積的符號就是[]

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因此這就表示長方形ABCD的面積

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長方形ABCD的面積就是

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其可盛下的邊長爲1的正方形的數量

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那我們就畫畫試試看

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我相信大家都會有更簡單的方法

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但我還是來演示下

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就比如

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這邊可以放7個邊長爲1的正方形 那邊可以放7個

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我會盡力畫整齊點

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這就是1 2 3 4 5 6 7個

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如果在一邊

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如果我們先算一邊

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那麽可以放下7個邊長爲1的正方形 就像這樣

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那邊可以放幾個呢

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這是1行

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兩行

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3行 4行 5行

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總共5行

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這樣就對了

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5個1相加是5

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7個1相加爲7

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總共7個

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這就是長7寬5的長方形

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你可以數一共有多少個

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也就是個簡單的乘法

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如果想知道有多少個小方格

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你可以屬

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可以看出有5行7列

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總共有35個

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小方格

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這邊有5個

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這邊有7個

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總計有35個

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因此這個長方形的面積是35

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那麽方法就是

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長乘以寬

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如果說有個長方形

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長爲2 寬爲1/2

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就是這樣大小

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你可以直接將它們相乘

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就是2乘1/2

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面積就是1

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你可能會問1/2什麽意思

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1/2指的就是你在這個方向只能放下半個長爲1的正方形

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如果畫出整個正方形

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看起來有點扭曲

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就是這樣

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我只畫了一半

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再像這樣 做另一半

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把兩部分相加

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就得到一整個正方形

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那麽正方形的面積怎麽求呢

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正方形比較特殊 因爲它長寬相等

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因此如果有個正方形

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我在這兒畫個正方形

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稱頂點爲x y z

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第四個點就叫s吧

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假設我要求面積

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假設這邊長爲2

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即xs長爲2

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求正方形xyzs的面積

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我用[]來指代面積

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這個多邊形

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我們知道這是個正方形

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所有邊都相等

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是長方形的特殊情況

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我們用長乘寬

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而長寬相等

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這是2 那也是2

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因此就是2乘2

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或2的平方

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這也就是平方的來源

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平方某物

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2乘2

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等於2的平方

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這就是平方的來源

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求正方形的面積

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就等於4

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可以看出你可以在這個長爲2的正方形中

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放4個長爲1的正方形