Q. 154.3( 4 Votes )

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

Answer :

Given: Perimeter of rhombus = 80 m

One of the diagonal = 24 m


To Find: Area of the rhombus


Concept Used:


If sides of a triangle are a, b, and c, then area of a triangle is given by:



Where s = semiperimeter of the triangle



The perimeter of rhombus = 4 × side of the rhombus


Diagram:



Explanation:


80 = 4 × side of the rhombus


The side of rhombus = 20 m


Clearly, Δ ACD and Δ ACB are congruent and thus their areas will also be equal.


Let us calculate the area of Δ ACD,




s = 32 m





Area = 16 × 12 m2


Area of Δ ACD = 192 m2.


Therefore,


Area of rhombus ABCD = Area of Δ ACD + Area of Δ ACB


Area of rhombus ABCD = (192 + 192) m2


Hence, Area of a rhombus is 384 m2.


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