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₪ Diketahui

1. BD = 24 cm, AB = 13 cm, K = 66 cm

2. d1 = 12 cm, K = 40 cm

? Ditanya

1. AC

2. Luas Belah Ketupat

✏ Penyelesaian

1. Panjang AO

AO² = AB² – BO²

AO² = AB² – ( BD ÷ 2 )²

AO² = 13² – ( 24 ÷ 2 )²

AO² = 13² – 12²

AO² = 169 – 144

AO² = 25

AO = √25

AO = 5 cm

Panjang CD ( sama dengan BC )

K = AB + AD + CD + BC

66 = 13 + 13 + 2CD

66 = 26 + 2CD

2CD = 40

CD = 20 cm

Panjang CO

CO² = CD² – DO²

CO² = 20² – ( BD ÷ 2 )²

CO² = 20² – ( 24 ÷ 2 )²

CO² = 20² – 12²

CO² = 400 – 144

CO² = 256

CO = √256

CO = 16 cm

Panjang AC

= AO + CO

= 5 cm + 16 cm

= 21 cm

2. K = 4s

40 = 4s

s = 10 cm

Panjang Diagonal

a² = b² – c²

a² = 10² – ( 12 ÷ 2 )²

a² = 100 – 36

a = √64

a = 8 cm

d2 = 2a

= 2 × 8

= 16 cm

Luas Belah Ketupat

= ½ × d1 × d2

= ½ × 12 × 16

= 6 × 16

= 96 cm²