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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