THIS IS BRAINLIEST QUESTION.
Answers
Step-by-step explanation:
the area of the rhombus is 4× side
the area of rhombus is 244.
Hey there,
Please find below the answer to your given question.
Given:
A rhombus ABCD where:
i) AB = BC = CD = AD = 61 cm
ii) Diagonals AC and BD = 22 cm intersect at O.
To Find:
i) AC
ii) ar(ABCD)
Solution:
Diagonals of a Rhombus bisect each other at 90°.
=> ∠COD = 90°, BO = DO = 22/2 = 11cm, AO = CO
In right ΔCOD,
OD² + OC² = CD²
=> 11² + OC² = 61²
=> 121 + OC² = 3721
=> OC² = 3721 - 121
=> OC² = 3600
=> OC = 60 cm.
But, Diagonal AC = OC + AO
=> AC = OC + OC [ OC = OA, as proved above]
=> AC = 2OC
=> AC = 2(60)
=> AC = 120 cm
We know, ar(Rhombus) = (Diagonal 1 x Diagonal 2)/2
ar(ABCD) = (AC x BD)/2
=> 22 * 120 /2
=> ar(ABCD) = 1320 sq. cm
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Hope it helps.
Have a great day! ;)