Question
A rhombus has an area of 1,800 cm², and its diagonals are
in the ratio 6:5. A circle is drawn using the smaller diagonal as its diameter. What is the difference between the area of the circle and 75% of the area of the rhombus? (Take π = 3)Solution
ATQ,
Let diagonals = 6x and 5x
Area = (1/2) × 6x × 5x = 15x²
1800 = 15x² → x² = 120 → x = √120 ≈ 10.95
Smaller diagonal = 5x ≈ 54.75 cm
Radius ≈ 27.375 cm
Area of circle ≈ 3 × (27.375)² ≈ 3 × 749.3 ≈ 2247.9 cm²
75% of rhombus = 0.75 × 1800 = 1350 cm²
Difference ≈ 2247.9 - 1350 = 897.9 cm²
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