Question

Tentukan Lp bangun di atas!

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Answer 1

Verified answer

Diketahui:

Prisma segitiga:

• a = AE = 5 cm
• m = AB = 13 cm
• t = BE = √(13² - 5²) = √(169 - 25) = √144 = 12 cm
• Tp = BG = DI = 30 cm

Prisma trapesium:

• a = BE = 12 cm
• b = CD = 20 cm
• t = BC = 15 cm
• m = JI = 17 cm
• Tp = DI = 30 cm

Ditanyakan:

• Lp gabungan = ... cm²?

Penyelesaian:

Rumus Luas Permukaan Prisma:

Lp = (2 × La) + (Ka × Tp)

• Prisma segitiga:

La = ½ × a × t

= ½ × 5 × 12

= 6 × 5

= 30 cm²

Ka = a + t + m

= 5 + 12 + 13

= 30 cm

• Prisma trapesium:

La = ½ × (a + b) × t

= ½ × (12 + 20) × 15

= ½ × 32 × 15

= 16 × 15

= 240 cm²

Ka = a + b + t + m

= 12 + 20 + 15 + 17

= 64 cm

• Luas permukaan gabungan:

Lp gabungan

= Lp prisma segitiga + Lp prisma trapesium

= [(2 × 30) + (30 × 30)] + [(2 × 240) + (64 × 30)]

= [60 + 900] + [480 + 1.920]

= 960 + 2.400

= 3.360 cm²

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