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Perhatikan gambar! Luas bangun ABCDE adalah ....

Perhatikan gambar!



Luas bangun ABCDE adalah ....

  1. begin mathsize 14px style 430 space cm squared end style 

  2. begin mathsize 14px style 470 space cm squared end style 

  3. begin mathsize 14px style 500 space cm squared end style 

  4. begin mathsize 14px style 568 space cm squared end style 

Jawaban:

Perhatikan gambar berikut!



 

Perhatikan segitiga CBD. Dengan menerapkan Teorema Pythagoras diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row BD equals cell square root of CD squared minus BC squared end root end cell row blank equals cell square root of 25 squared minus 15 squared end root end cell row blank equals cell square root of 625 minus 225 end root end cell row blank equals cell square root of 400 end cell row blank equals cell 20 space cm end cell end table end style 

Perhatikan segitiga BFD. Dengan menerapkan Teorema Pythagoras diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row FD equals cell square root of DD squared minus BF squared end root end cell row blank equals cell square root of 20 squared minus 16 squared end root end cell row blank equals cell square root of 400 minus 256 end root end cell row blank equals cell square root of 144 end cell row blank equals cell 12 space cm end cell end table end style 

Bangun di atas terdiri dari trapesium ABDE dan segitiga CBD. Dengan menerapkan rumus luas trapesium dan segitiga, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript ABCDE end cell equals cell straight L subscript ABDE plus straight L subscript CBD end cell row blank equals cell fraction numerator AB plus ED over denominator 2 end fraction times AE plus fraction numerator BC times CD over denominator 2 end fraction end cell row blank equals cell fraction numerator 14 plus open parentheses 14 plus 12 close parentheses over denominator up diagonal strike 2 end fraction times up diagonal strike 16 to the power of space 8 end exponent plus fraction numerator 15 times up diagonal strike 20 to the power of space 10 end exponent over denominator up diagonal strike 2 end fraction end cell row blank equals cell 40 times 8 plus 15 times 10 end cell row blank equals cell 320 plus 150 end cell row blank equals cell 470 space cm squared end cell end table end style 

Jadi, luas bangun ABCDE adalah begin mathsize 14px style 470 space cm squared end style.

Dengan demikian, jawaban yang tepat adalah B.

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