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Pertanyaan

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Panjang begin mathsize 14px style A B equals 6 space c m comma space A C equals 10 space c m comma space text dan end text space A D equals 12 space c m end style. Tentukan luas begin mathsize 14px style triangle A C D end style!

Pembahasan Soal:

Luas segitiga begin mathsize 14px style A C D end style dapat ditentukan sebagai berikut.

begin mathsize 14px style text L end text subscript A C D end subscript equals text L end text subscript A B D end subscript minus text L end text subscript A B C end subscript end style

Dengan teorema Pythagoras dapat ditentukan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell B C end cell equals cell square root of A C squared minus A B squared end root end cell row blank equals cell square root of 10 squared minus 6 squared end root end cell row blank equals cell square root of 100 minus 36 end root end cell row blank equals cell square root of 64 end cell row blank equals 8 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell B D end cell equals cell square root of A D squared minus A B squared end root end cell row blank equals cell square root of 12 squared minus 6 squared end root end cell row blank equals cell square root of 144 minus 36 end root end cell row blank equals cell square root of 108 end cell row blank equals cell 6 square root of 3 end cell end table end style

Luas segitiga begin mathsize 14px style A B C end style, yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell text L end text subscript A B C end subscript end cell equals cell 1 half cross times B C cross times A B end cell row blank equals cell 1 half cross times 8 cross times 6 end cell row blank equals 24 end table end style

Luas segitiga begin mathsize 14px style A B D end style, yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell text L end text subscript A B D end subscript end cell equals cell 1 half cross times B D cross times A B end cell row blank equals cell 1 half cross times 6 square root of 3 cross times 6 end cell row blank equals cell 18 square root of 3 end cell end table end style

Luas segitiga undefined, yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell text L end text subscript A C D end subscript end cell equals cell text L end text subscript A B D end subscript minus text L end text subscript A B C end subscript end cell row blank equals cell 18 square root of 3 minus 24 end cell end table end style

Dengan demikian, luas begin mathsize 14px style triangle A C D end style adalah begin mathsize 14px style open parentheses 18 square root of 3 minus 24 close parentheses space text cm end text squared end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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