find the area of Rhombus if the measure of each side is 26 cm and one of its diagonal is 48 centimetre
Answers
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
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Also View:
If the area of a rhombus is 48 cm and one of its diagonals is 12 cm find the side of the rhombus ?
https://brainly.in/question/268647
Find the area of a rhombus, one side of which measures 20 cm.and one diagonal is 24 cm.
https://brainly.in/question/1426351
The area of a rhombus is 480cmsquare, and one of its diagonals measures 48cm. find(1) the length of the other diagonals,(2) the length of each of its sides, and (3) it's perimeter.
https://brainly.in/question/5021012
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
--------------------------------------------------------------------------------------
Also View:
If the area of a rhombus is 48 cm and one of its diagonals is 12 cm find the side of the rhombus ?
brainly.in/question/268647
Find the area of a rhombus, one side of which measures 20 cm.and one diagonal is 24 cm.
brainly.in/question/1426351
The area of a rhombus is 480cmsquare, and one of its diagonals measures 48cm. find(1) the length of the other diagonals,(2) the length of each of its sides, and (3) it's perimeter.
brainly.in/question/5021012