Jawaban:

Diketahui :

• panjang diagonal 1 (d1) = 16 cm
• panjang diagonal 2 (d2) = 30 cm
• Volume = 9600 cm³

Ditanya :

• Luas permukaan (Lp) prisma = .....?

Dijawab :

1. Tentukan tinggi (t) prisma

Volume = Luas alas x tinggi

Volume = 1/2 x d1 x d2 x t

9600 = 1/2 x 16 x 30 x t

9600 = 8 x 30 x t

9600 = 240 x t

t = 9600/240

t = 40 cm

2. Tentukan panjang sisi (s) prisma

s² = (1/2 d1)² + (1/2 d2)²

s² = (1/2 x 16)² + (1/2 x 30)²

s² = 8² + 15²

s² = 64 + 225

s² = 289

s = √289

s = 17 cm

3. Tentukan Luas permukaan (Lp) prisma

Lp prisma = luas alas + 2(keliling alas x tinggi)

Lp prisma = (1/2 x d1 x d2) + 2 (4s x t)

Lp prisma = (1/2 x 16 x 30) + 2 ((4 x 17) x 40))

Lp prisma = (8 x 30) + 2 (68 x 40)

Lp prisma = 240 + 2 (2720)

Lp prisma = 240 + 5440

Lp prisma = 5680 cm²