Question

find the area of a rhombus if the measure of each side is 26 cm and its diagonal is 48 CM.


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Answer 1

Answer:

The area of the rhombus is 480 cm².

Step-by-step explanation:

Referring to the figure attached below, we have

ABCD is a rhombus

Each side of a rhombus, AB = BC = CD = DA = 26cm

One of the diagonal, AC = 48 cm

We know that the diagonals of a rhombus bisect each other at right angles.

∴ ∠AOB = ∠BOC = ∠COD = ∠DOA = 90°

and

∴ OA = OC = ½ * AC = ½ * 48 = 24 cm

Now, considering ∆ AOB and applying Pythagoras theorem, we get

AB² = OB² + OA²

⇒ OB = √[AB² – OA²]

⇒ OB = √[26² – 24²]

⇒ OB = √[100]

⇒ OB = 10 cm

∴ OB = OD = 10 cm

∴ Other diagonal of the rhombus, BD = 2 * OB = 10 * 2 = 20 cm

Thus,

The area of the rhombus ABCD,

= ½ * AC * BD

= ½ * 48 * 20

= 10 * 48

= 480 cm²

Step-by-step explanation:

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Answer 2

Answer:

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