find the area of a rhombus having each side equal to 20 cm and one of its diagonals equal to 24 cm
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According to the question,
AB = BC = CD = AD = 20 cm
Consider, DB = 24 cm
As diagonals of rhombus bisect each other.
DO = OB = 12 cm
In triangle AOB,
AO² + OB² = AB²
AO² + 12² = 20²
AO² = 400 - 144 = 256
AO = 16 cm
Diagonal AC = 16 × 2 = 32 cm
Area of the rhombus = 1/2 × AC × BD
= 1/2 × 32 × 24
= 384 cm²
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