Question

A rhombus has a perimeter of 68 cm and diagonal of 30 cm . Find the area of the rhombus

Answer 1

Heya !!!




Let ABCD is a rhombus .



In which,




AB = BC = CD = AD






Given that,




Perimeter of rhombus ABCD = 68



4 × Side = 48


Side = 48/4




Side = 12 cm




Let AC = 30 cm


As we know that,




Diagonal of rhombus bisect each other at right angled



So,.



OA = OC = 1/2 AC



OA = OC = 1/2 × 30



OA = OC = 15 cm



In right angled triangle OAB







AB² = (OA)² + (OB)²





(OB)² = (AB)² - (OA)²





(OB)² = (12)² - (15)²






(OB)² = 144 - 225





OB = root (-81)




OB = 9 cm





Therefore,



BD = 2 × OB = 2 × 9 = 18 cm









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






=> 1/2 × ( 30 × 18)







=> 540/2





=> 270 cm².




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Answer 2

area of diagonal 240 cmy