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

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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