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解けそうで解けない面積の問題その1

2018年2月21日 塾長からの挑戦状

 

三平方の定理を知っている人はゴリゴリ計算して解くこともできますが,実は小学5年生でも解くことができます。中学入試では有名な形だったりします。

こたえはこの下

こたえ

∠BADと∠DCBの和は180度で,AD=CDなので,上の図のように四角形ABCDを90度回転させながら4枚つなげると大きな四角形ができます。それも,4つの辺がすべて8cm,4つの角がすべて90度なので正方形ですね。求める面積は,この正方形の面積の4分の1なので,

8×8÷4=16(㎠)

となります。

「辺の長さが同じ」と聞くとどうしても二等辺三角形を連想しがちですが,このように同じ図形をもう1枚くっつけたり,切り離してくっつけたりすると有名な形になることがあります。「辺の長さが同じ」という条件をどう利用するのか分からないときは試してみるのも良いでしょう。

 

%d人のブロガーが「いいね」をつけました。