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L subscript p equals horizontal ellipsis space cm squared

V equals horizontal ellipsis space cm cubed

Pembahasan Soal:

Rumus volume limas adalah

straight V subscript limas equals 1 third cross times straight L subscript alas cross times t subscript limas

Karena alas berbentuk persegi panjang, maka luasnya adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript alas end cell equals cell AB cross times BC end cell row blank equals cell 36 space cm cross times 20 space cm end cell row blank equals cell 720 space cm squared end cell end table

Dengan demikian, volume limas segitiga adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight V subscript limas space segiempat end subscript end cell equals cell 1 over up diagonal strike 3 to the power of 1 cross times 720 space cm squared cross times up diagonal strike 24 to the power of 8 space cm end cell row blank equals cell 5.760 space cm cubed end cell end table

Selanjutnya, perhatikan pada gambar berikut:



 

triangle TOP siku-siku di O, karena tinggi limas TO tegak lurus alas ABCD. Panjang O P equals 1 half AB equals 18 space cm. Dengan menggunakan dalil Pythagoras, panjang TP adalah

table attributes columnalign right center left columnspacing 0px end attributes row TP equals cell square root of TO squared plus OP squared end root end cell row blank equals cell square root of open parentheses 24 space cm close parentheses squared plus open parentheses 18 space cm close parentheses squared end root end cell row blank equals cell square root of 576 space cm squared plus 324 space cm squared end root end cell row blank equals cell square root of 900 space cm squared end root end cell row blank equals cell 30 space cm end cell end table

sehingga luas triangle TBC adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript TBC end cell equals cell fraction numerator BC cross times TP over denominator 2 end fraction end cell row blank equals cell fraction numerator up diagonal strike 20 to the power of 10 space cm cross times 30 space cm over denominator up diagonal strike 2 to the power of 1 end fraction end cell row blank equals cell 300 space cm squared end cell end table

Karena alas triangle TAD adalah AD equals BC equals 20 space cm, maka luas triangle TAD juga 300 space cm squared.

Berikutnya, perhatikan gambar berikut:


triangle TOR siku-siku di O. Panjang OR equals 1 half B C equals 10 space cm. Dengan menggunakan dalil Pythagoras, panjang TR adalah

table attributes columnalign right center left columnspacing 0px end attributes row TR equals cell square root of TO squared plus OR squared end root end cell row blank equals cell square root of open parentheses 24 space cm close parentheses squared plus open parentheses 10 space cm close parentheses squared end root end cell row blank equals cell square root of 576 space cm squared plus 100 space cm squared end root end cell row blank equals cell square root of 676 space cm squared end root end cell row blank equals cell 26 space cm end cell end table

sehingga luas triangle TCD adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript TCD end cell equals cell fraction numerator CD cross times TR over denominator 2 end fraction end cell row blank equals cell fraction numerator up diagonal strike 36 to the power of 18 space cm cross times 26 space cm over denominator up diagonal strike 2 to the power of 1 end fraction end cell row blank equals cell 468 space cm squared end cell end table

Karena alas triangle TAB adalah AB equals CD equals 36 space cm, maka luas triangle TAB juga 468 space cm squared.

Akibatnya luas sisi tegak limas T point ABCD adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript sisi space tegak end subscript end cell equals cell straight L subscript TAB plus straight L subscript TBC plus straight L subscript TCD plus straight L subscript TAD end cell row blank equals cell open parentheses 468 plus 300 plus 468 plus 300 close parentheses space cm squared end cell row blank equals cell 1.536 space cm squared end cell end table

sehingga luas permukaan limas T point ABCD adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript straight T. ABCD end subscript end cell equals cell straight L subscript alas plus straight L subscript sisi space tegak end subscript end cell row blank equals cell 720 space cm squared plus 1.536 space cm squared end cell row blank equals cell 2.256 space cm squared end cell end table

Jadi, volume limas T point ABCD adalah 5.760 space cm cubed dan luas permukaannya adalah 2.256 space cm squared.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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