Each side of a rhombus is 26 cm and one of its diagonals is 48 cm long. The area of the
rhombus is:
(a) 240 cm? (b) 300 cm? (c) 360 cm? (d) 480 cm?
Answers
Answer:
s=26,d=48
Step-by-step explanation:
1/2d√4ssquare-d
1/2*48√4*26*26-48
=480cm
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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