What is the maximum area of a rectangle which can be inscribed in a c…

The correct answer is Option (2) → 8 cm²

Every rectangle drawn inside a circle with its corners on the circle has a diagonal equal to the diameter. Among rectangles with a given diagonal, the square has the largest area.

• Diagonal \(=\) diameter \(=4\) cm

• Side of the square \(\displaystyle=\frac{4}{\sqrt{2}}=2\sqrt{2}\) cm

• Area \(=(2\sqrt{2})^2=8\) cm²

Shortcut:

• The area of a square is half the square of its diagonal: \(\displaystyle\frac{4^2}{2}=8\) cm², that is \(2r^2\) for a circle of radius \(r\).