Question
A rhombus has an area of 2,592 cm² and its diagonals are
in the ratio 5:3. A circle is drawn with the shorter diagonal of the rhombus as its diameter. Calculate the difference between the area of the circle and 75% of the rhombus’s area. (Take π = 3)Solution
ATQ,
Let diagonals = 5x and 3x
(1/2) × 5x × 3x = 7.5x²
2592 = 7.5x² → x² = 345.6 → x = √345.6 ≈ 18.59
Smaller diagonal = 3x ≈ 55.77 cm
Radius ≈ 27.89 cm
Area of circle ≈ 3 × (27.89)² ≈ 3 × 778.4 ≈ 2335.2 cm²
75% of rhombus = 0.75 × 2592 = 1944 cm²
Difference ≈ 2335.2 - 1944 = 391.2 cm²
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