Question

find the area of rhombus whose perimeter is 200 m and one of its diagonal is 80 m

Answer 1

Heya !!!






Perimeter of rhombus = 200 m




4 × Side = 200




Side = 200/4




Side = 50 m





Let AC = 80 m




We know that,


Diagonal of rhombus bisect each other at right angles.




Therefore,



OA = OC = 1/2 × AC




OA = OC = 40 m




By pythagoras theorem ,



AB² = under root OA² + OB





(50)² = (40)² + OB²



OB² = (50)² - (40)²




OB² = 2500 - 1600




OB² = 900




OB = root 900



OB = 30 m



Therefore,



BD = 2 × OB




BD = 2 × 30 = 60 m





We know that,




Area of triangle = 1/2 × (Product of diagonals)





=> 1/2 × ( AC × BD)





=> 1/2 ×( 80 × 60)





=> 2400 m²



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