A rectangle with one side 4 cm is inscribed in a circle of radius 2.5 cm. Find the area of the rectangle.
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Question

A rectangle with one side 4 cm is inscribed in a circle of radius 2.5 cm. Find the area of the rectangle.

KnowledgeBoat · Accepted 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.

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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