find the aera of rhombus if measure of each side id 26 cm and one of its diagonals is 48 cm
Answers
Answer:
139 cm²
Step-by-step explanation:
AB = 26 cm
AC = 48 cm
we know that diagonal of rhombus bisect. join BD which intersect AC at O
so AO = 24 cm
In triangle AOB BY PYTHAGORAS THEOREM
AB²=AO²+OB²
AB²-AO²=OB²
(26)²-(24)²=OB²
(26+24)(26-24)=OB²
50×2=OB²
100=OB²
OB= √100
OB=10cm
so we know BO=OD SO BD= 20 cm
area of a rhombus ABCD= 1/2×26×20=13×10=130cm²
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 ?
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
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