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Mathematics Senior High

よっての所のs=2△abdのabdがなぜくるのですか? 優しい方詳しく説明教えてください

基本例題159 図形の分割と面積 (1) 次のような四角形ABCD の面積Sを求めよ。 8日 平行四辺形ABCD で, 対角線の交点を0とすると (1) AC=10, BD=6√2,∠AOD=135° (2) AD//BC の台形 ABCD で, AB=5,BC=8, BD=7,∠A=120° 指針 四角形の面積を求める問題は, 対角線で2つの三角形に分割して考える。 (1) 平行四辺形は,対角線で合同な2つの三角形に分割されるから S=2△ABD また, BO=DO から △ABD = 2AOAD よって, まず △OADの面積を求める。 (2) 台形の面積=(上底+下底)×高さ÷2 が使えるように, 未知の量である上底ADの 長さと高さを求める。 まず, △ABD (2辺と1角が既知) において余弦定理を適用。 CHART 四角形の問題 対角線で2つの三角形に分割 解答 (1) 平行四辺形の対角線は, 互いに他を2等分するから A=1/AC=5, OD= D=1/2BD=3√2 A 合 したがって AOAD= OA-OD sin 135° 15 2 AD²+5AD-24-0 (AD-3)(AD+8)=0 135° ゆえに よって AD > 0 であるから AD=3 頂点Aから辺BCに垂線 AHを引くと AJOX ) △ABD において, 余弦定理により 72=52+AD²-2・5・AD cos 120°割する120% 5 7 B = 1/2.5-3√/2 √/2= 1つにしちゃ よって S=2△ABD=2・2△OAD=4.15=30X[練習 159 (2)参照] pbe 42 S=AC-BD sin B H D p.245 基本事項 2. 基本 158 (RA+I) Danis AH = ABsin∠B, ∠B=180°∠A=60° CELE 851 8 527 S=²(AD+BC)AH=(3+8).5 sin 60°= C (*) △OAB と △OAD は, それぞれの底辺をOB, OD とみると, OB=OD で, 高さ が同じであるから、その面積 も等しい。 [参考] 下の図の平行四辺形の 面積Sは 55√3 4 247 B | AD // BC C (上底+下底)×高さ÷2

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English Senior High

(2)にはbeingが入るのですがなんでそうなののかがわかりません。周辺の文構造も一緒に解説していただけるとありがたいです

(1) Considerable attention has been paid to the size or relative size of the human brain. The first point of interest is that the ratio of brain weight to body is at a maximum at birth and decreases with age, reaching a fairly steady level by maturity. In other 5 words, newborn babies have very large brains, relatively speaking, weighing some 300 grams. This is roughly the size of the brain of an adult male chimpanzee. Children and their brains continue to grow for many years, gradually increasing their ability to learn and remember. There have been suggestions that the growth of 10 the brains of children is not steady, but occurs suddenly, each period of rapid growth (2) associated with a particularly important developmental or intellectual stage. These stages could be the ability to reason abstractly, to talk, or even to do arithmetic. The idea of sudden brain growth is still around, but 15 has not attracted much enthusiasm. Some research has shown differences in the relative sizes of the brains of males and females of the same age, but so far no great differences have been found between people of the same age but of different ethnic groups. Obviously the brain of a small Japanese teenager is very much smaller than that of a giant Russian boy. But when brain size is adjusted for size or weight of the body, there ( 3 ) great advantage for either with respect to intelligence. Moreover, in measuring intelligence one has, of course, to take into account the effects of education and cultural background. Individual brain sizes, particularly of famous people, have also

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