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

Given, rectangle ABCD is inscribed in a circle of radius 2.5 cm

Let AB = 4 cm

Now, OA = OC = 2.5 cm [Radius of circle]

⇒ AC = OA + OC = 2.5 + 2.5 = 5 cm

In right triangle ABC, by Pythagoras theorem

(AC)² = (AB)² + (BC)²

⇒ 5² = 4² + (BC)²

⇒ BC² = 25 – 16 = 9

⇒ BC = 3 cm

∴ Area of rectangle = AB × BC = 4 × 3 = 12 cm²