Q6 of 50 Page 12

Find the area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m.

Let ABCD be the rhombus of perimeter 80 m and diagonal AC = 24 m


We have,


AB + BC + CD + DA = 80


4 AB = 80 [AB=BC=CD=DA sides of Rhombus]


AB = 20 m



In ΔABC, we have


AB = a = 20 cm, BC = b = 20 cm, AC = c = 24 cm


Let a, b and c are the sides of triangle and s is


the semi-perimeter, then its area is given by:


A = where [Heron’s Formula]


= = 32


A=


A = = cm2


Hence, area of rhombus ABCD = 2 ×192 m2


= 384 m2


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