Question

the area of square that can be inscribed in a circle of radius 12cm is​

Answer 1

So clearly from the diagram the maximum a diagonal of such square can be of is of diameter of circle i.e 24 cm here.

Ans as we know that,
$digonal \: of \: square = \sqrt{2}a$
(where a is the measure of one side)

Using this relation measure of one side of the square will be given by,
$\sqrt{2} a = 24 \\ a = \frac{24}{ \sqrt{2} } = 12 \sqrt{2}$


Now the area of the square will be,
${(12 \sqrt{2}) }^{2}{cm}^{2}\\ = 144 \times 2{cm}^{2}\\ = 288 \: {cm}^{2}$


Hence your answer.