Penyelesaian
[tex]AD= \sqrt{(13 \times 13) + (5 \times 5)} \\ = \ \sqrt{169 + 25} \\ =√144 \\ =12[/tex]
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[tex]AC= \sqrt{(15 \times 15) - (12 \times 12)} \\ = \: \sqrt{(225 - 144} \\ = \sqrt{81} \\ = 9[/tex]
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[tex]L1= \frac{1}{2} ×5×12 \\ =5 \times 12 \\ = 30[/tex]
[tex]L2= \frac{1}{2} ×12×15 \\ =12 \times 15 \\ =90[/tex]
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Maka Luas seluruh Limas segitiga adalah
30+90
=120
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Detail Jawaban :
Mapel : MTK
Kelas : 8smp
materi : bangun ruang limas segitiga
kode soal : 2
kode kategorisasi : 8.2.2
Cari panjang AD:
- AD² = AB² - BD²
- AD² = 13² - 5²
- AD² = 169 - 25
- AD² = 144
- AD = √144
- AD = 12 cm
[tex] \: \: [/tex]
Luas segitiga ABC
= luas segitiga ABD + luas segitiga ADC
= (½ × BD × AD) + (½ × CD × AD)
= (½ × 5 × 12) + (½ × 15 × 12)
= (5 × 6) + (15 × 6)
= 30 + 90
= 120 cm²
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