こんにちは。立体の問題です。早速取り組んでいきましょう。
【問題】三角錐があります。
,
とし,
となる点Eを辺
上にとります。三角形OABの面積が
のとき, 次の問いに答えなさい。
(1) 三角形OCEと三角形ACEの面積比を求めなさい。
![Rendered by QuickLaTeX.com \text{OF}=\text{OG}=2\,\text{cm}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-3a9ca037fea9d8b999e4dd1debe6d53b_l3.png)
(2) 底面を三角形EFGとするとき, 三角錐
![Rendered by QuickLaTeX.com \mathrm{O-EFG}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-d931fd2753cf0c694ceea809c684aa4b_l3.png)
(3) 四角錐
![Rendered by QuickLaTeX.com \mathrm{E-BCGF}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-f34aed73f15229835dbccf695da5fe0c_l3.png)
![Rendered by QuickLaTeX.com O-ABC](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-ec3de65c17dc19eff8f9f0283dce0b9d_l3.png)
【麗澤中第一回AE】
【解答例】
(1) なので,
(答)
(2)
![Rendered by QuickLaTeX.com \bigtriangleup\text{OAB}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-ec17ed95f99acafffe076067e3cae674_l3.png)
![Rendered by QuickLaTeX.com \bigtriangleup\text{OEF}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-653a520d85ac5e9348705f5d24c1a101_l3.png)
相似比は
![Rendered by QuickLaTeX.com 5 : 2](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-7d59a05cd2dd1d835bfad6b53ae33722_l3.png)
![Rendered by QuickLaTeX.com 25 : 4](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-55bedb0220a7c3cbf9d71e06bcb6745d_l3.png)
![Rendered by QuickLaTeX.com \bigtriangleup\text{OAB}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-ec17ed95f99acafffe076067e3cae674_l3.png)
![Rendered by QuickLaTeX.com 12\text{cm}^2](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-cfdf8d73af677625b887299cf2d3eea8_l3.png)
![Rendered by QuickLaTeX.com \bigtriangleup\text{OEF}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-653a520d85ac5e9348705f5d24c1a101_l3.png)
![Rendered by QuickLaTeX.com 12\times\dfrac{4}{25}=\dfrac{48}{25}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-5812d4be5ac2e10ad1b61c684c6a2c48_l3.png)
よって求める側面積は,
![Rendered by QuickLaTeX.com \dfrac{48}{25}\times3=\dfrac{144}{25}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-2b82f3e1f296248cdd3cc998f5ec86d0_l3.png)
![Rendered by QuickLaTeX.com \dfrac{144}{25}\text{cm}^2\cdots](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-d1e9b8d5bacb8ca7c56e6994b706d7f4_l3.png)
(3)
三角錐
![Rendered by QuickLaTeX.com \mathrm{O-ABC}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-881299798daf2446c397c89dbdf8b20c_l3.png)
三角錐
![Rendered by QuickLaTeX.com \mathrm{O-ABC}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-881299798daf2446c397c89dbdf8b20c_l3.png)
![Rendered by QuickLaTeX.com \mathrm{O-EFG}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-d931fd2753cf0c694ceea809c684aa4b_l3.png)
![Rendered by QuickLaTeX.com 5 : 2](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-7d59a05cd2dd1d835bfad6b53ae33722_l3.png)
![Rendered by QuickLaTeX.com 125 : 8](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-0cf9626c5636dea1489caf3cb59a04f1_l3.png)
![Rendered by QuickLaTeX.com \mathrm{O-EFG}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-d931fd2753cf0c694ceea809c684aa4b_l3.png)
![Rendered by QuickLaTeX.com 1\times\dfrac{8}{125}=\dfrac{8}{125}\cdots\maru1](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-9189c1c01b416b8e4d3cdf8b4a997b17_l3.png)
三角錐
![Rendered by QuickLaTeX.com \mathrm{E-ABC}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-c5f398373b6711f474c3ca11cf8af632_l3.png)
![Rendered by QuickLaTeX.com \mathrm{O-ABC}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-881299798daf2446c397c89dbdf8b20c_l3.png)
![Rendered by QuickLaTeX.com \dfrac35](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-e16cfb4d8e93d52a5d05338e78b09899_l3.png)
![Rendered by QuickLaTeX.com 1\times\dfrac35=\dfrac35\cdots\maru2](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-a80d08ad952085c8fe9d8817fcfcc28c_l3.png)
![Rendered by QuickLaTeX.com \maru1, \maru2](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-17f7275e5547cb30256f14fe6f9231f7_l3.png)
![Rendered by QuickLaTeX.com \mathrm{E-BCGF}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-f34aed73f15229835dbccf695da5fe0c_l3.png)
![Rendered by QuickLaTeX.com 1-\dfrac{8}{125}-\dfrac35=\dfrac{42}{125}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-ea54df7a657bfe486e9e84bd3d8b7eec_l3.png)
よって, 四角錐
![Rendered by QuickLaTeX.com \mathrm{E-BCGF}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-f34aed73f15229835dbccf695da5fe0c_l3.png)
![Rendered by QuickLaTeX.com O-ABC](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-ec3de65c17dc19eff8f9f0283dce0b9d_l3.png)
![Rendered by QuickLaTeX.com \dfrac{42}{125} : 1 = 42 : 125](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-3a599531abc73590585d0cb1ffd0bd00_l3.png)
![Rendered by QuickLaTeX.com 42 : 125\cdots](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-0d8da318819866ae0a1b1779dcdaf4cc_l3.png)
こんにちは。立体の問題です。早速取り組んでいきましょう。
【問題】三角錐があります。
,
とし,
となる点Eを辺
上にとります。三角形OABの面積が
のとき, 次の問いに答えなさい。
【解答例】
(1) なので,
(答)
(2)