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Persegi panjang ABCD dan EFGH sebangun. Luas daerah yang diarsir .... begin mathsize 14px style cm squared end style 

  1. begin mathsize 14px style 150 end style 

  2. begin mathsize 14px style 183 end style 

  3. begin mathsize 14px style 318 end style 

  4. begin mathsize 14px style 381 end style 

Jawaban:

Perhitungan luas daerah yang diarsir sebagai berikut:

Langkah 1: Mencari luas segitiga begin mathsize 14px style EDH end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript increment EDH end subscript end cell equals cell fraction numerator straight a cross times straight t over denominator 2 end fraction end cell row blank equals cell fraction numerator ED cross times DH over denominator 2 end fraction end cell row blank equals cell fraction numerator 9 cross times 12 over denominator 2 end fraction end cell row blank equals cell 54 blank cm squared end cell end table end style 

Langkah 2: Mencari luas segitiga begin mathsize 14px style GCH end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript increment GCH end subscript end cell equals cell fraction numerator straight a cross times straight t over denominator 2 end fraction end cell row blank equals cell fraction numerator GC cross times CH over denominator 2 end fraction end cell row blank equals cell fraction numerator 16 cross times 12 over denominator 2 end fraction end cell row blank equals cell 96 blank cm squared end cell end table end style 

Langkah 3: Mencari luas persegi panjang begin mathsize 14px style EFGH end style.

  • Mencari begin mathsize 14px style EH end style

table attributes columnalign right center left columnspacing 0px end attributes row EH equals cell square root of ED squared plus DH squared end root end cell row blank equals cell square root of 9 squared plus 12 squared end root end cell row blank equals cell square root of 81 plus 144 end root end cell row blank equals cell square root of 225 end cell row blank equals 15 end table 

maka panjang begin mathsize 14px style EH equals 15 blank cm end style.

  • Mencari begin mathsize 14px style GH end style 

table attributes columnalign right center left columnspacing 0px end attributes row GH equals cell square root of G C squared plus H C squared end root end cell row blank equals cell square root of 16 squared plus 12 squared end root end cell row blank equals cell square root of 256 plus 144 end root end cell row blank equals cell square root of 400 end cell row blank equals 20 end table 

maka panjang Error converting from MathML to accessible text..

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript EFGH end cell equals cell straight p cross times straight l end cell row blank equals cell GH cross times EH end cell row blank equals cell 20 cross times 15 end cell row blank equals cell 300 space cm squared end cell end table end style 

Langkah 4: Mencari luas persegi panjang begin mathsize 14px style ABCD end style.

  • Mencari BC

Karena persegi panjang ABCD dan EFGH sebangun, sehingga berlaku perbandingan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BC over GH end cell equals cell DC over EH end cell row cell BC over 20 end cell equals cell 24 over 15 end cell row cell 15 BC end cell equals cell 24 times 20 end cell row cell 15 BC end cell equals 480 row BC equals cell 32 space cm end cell end table end style 

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript ABCD end cell equals cell straight p cross times straight l end cell row blank equals cell BC cross times DC end cell row blank equals cell 32 cross times 24 end cell row blank equals cell 768 space cm squared end cell end table end style 

Langkah 5: Mencari luas daerah yang diarsir

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Luas blank yang blank diarsir end cell equals cell straight L subscript ABCD minus left parenthesis straight L subscript EFGH plus straight L subscript increment GCH end subscript plus straight L subscript increment EDH end subscript right parenthesis end cell row blank equals cell 768 minus open parentheses 300 plus 96 plus 54 close parentheses end cell row blank equals cell 768 minus 450 end cell row blank equals cell 318 space cm squared end cell end table end style 

Luas daerah yang diarsir adalah Error converting from MathML to accessible text..

Jadi, jawaban yang tepat adalah C.

 

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