Question

If the perimeter of a rhombus is 40 cm and one of its diagonal is 16 cm, then what is the area (in cm2) of the rhombus?

• A. 72
• B. 48
• C. 96
• D. 120

Answer 1

Answer:

C. 96

 

ABCD is the rhombus.

Perimeter = 40

Side = 40/4 = 10

AB = BC = CD = DA = 10 

BD = 16 

Diagonals of a rhombus diagonally bisects each other

In AEB we have

∠AEB = 90

BE = BD/2 = 8 

AB = 10 

AE = √ (10² – 8²) = √(100 – 64) = 6 

AC = 2 × AE = 2 × 6 = 12 

Area of the rhombus = ½ × 16 × 12 = 96