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 m^{2}

Area of Δ ACD = 192 m^{2}.

Therefore,

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

Area of rhombus ABCD = (192 + 192) m^{2}

**Hence, Area of a rhombus is 384 m ^{2}.**

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