1.

The diagonal of a rhombus are 26cm and 12cm.find its area and perimeter.

Answer» \huge{\mathcal{Hi\: there!}}

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\huge{\underline{\bold{Solution :}}}

Let the DIAGONALS of the rhombus be P and Q.

Given ; P = 26 cm and Q = 12 cm.

Area of rhombus = \mathsf{ \frac{pq}{2}}

Area of rhombus = 26 × 12 / 2

Area of rhombus = 312 / 2

Area of rhombus = 156 cm².

Now,
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Let us know first, the PROPERTIES of rhombus.

1. All sides of a rhombus are equal.

2. Diagonals of a rhombus bisect each other.

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According to QUESTION,

AC = 26 cm and BD = 12 cm.

And,

AE = EC = 13 cm.

BE = ED = 6 cm.

[see the above DIAGRAM]

Now,

In ΔAED, using pythagoras theorem,

We have ;

AD² = AE² + ED²

AD² = 13² + 6²

AD² = 169 + 36

AD² = 205

AD = √205

AD = 14. 31

As we know,

Each side of a rhombus are equal.

Therefore,

Perimeter = AD + DC + CB + BA

Perimeter = 14.31 × 4

Perimeter ≈ 57. 24 cm

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Thanks for the question!

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