Mathematics
A rectangle with one side 4 cm is inscribed in a circle of radius 2.5 cm. Find the area of the rectangle.
Mensuration
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Answer
Let ABCD be a rectangle with AB = 4 cm.
From figure,
Diameter of circle, AC = AO + OC = 2.5 + 2.5 = 5 cm.
In right angle triangle ABC,
⇒ AC2 = AB2 + BC2
⇒ 52 = 42 + BC2
⇒ BC2 = 52 - 42
⇒ BC2 = 25 - 16 = 9
⇒ BC = = 3 cm.
By formula,
Area of rectangle = l × b
= AB × BC
= 4 × 3
= 12 cm2.
Hence, area of rectangle = 12 cm2.
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