Question

the side of a rhombus I 10cm and one of its diagonal is 16cm long. The area of the rhombus is
a)96cm2 b)192cm2 c)160cm2 d)80cm2​

Answer 1

Answer :-

Area of the rhombus is a) 96 cm².

Step-by-step explanation :-

∅ In ABCD rhombus AB = 10 cm and AC = 16 cm :

AO = AC/2

AO = 16/2

AO = 8 cm

∅ In a rhombus, diagonals bisect each other perpendicularly :

In ΔAOD, ∠AOD = 90°

∅ Using Pythagoras theorem :

AD² = OA² + OD²

10² = 8² + OD²

100 = 64 + OD²

OD² = 36

OD = √36

OD = 6 cm

Diagonal BD = 2(OD)

• 2 × 6
• 12 cm

∅ Area of the rhombus :

1/2 × Diagonal1 × Diagonal2

1/2 × AC × BD

1/2 × 16 × 12

8 × 12

96 cm²

∴ Area of the rhombus is a) 96 cm².

Answer 2

Option a is the correct option.