How to do this? Thanks.

Source: ?

How to do this? Thanks.

Source: ?

mr.tan

This question looks difficult because 288 is not a square. But 144 is a square and 288 = 2 x 144 = 2 x 12 x 12. How can this help?FUN FACTConsider the blue square in the left diagram. It has side 2x and so its area is 4x^{2}. The pink square in the middle is half of the blue one so its area is 2x^{2}. Rotating it 45 degrees to get the right diagram. It tells us that if a square has area 2x^{2}, then its DIAGONALS (not the sides) is of length 2x.

Using this FUN FACT and also that the square in the question has area 2 x 12^{2}= 288 cm^{2}, we know its diagonal = 2 x 12 = 24. So it has radius 12.The area of the shaded part= area of circle - area of square= pi x 12The FUN FACT is often useful in competitions.^{2}- 288 = 164.16 cm^{2}.

Meema

Thank you! So much clearer now👍🏻😁

waterflow

If O is the centre of the circle and sqaure.

Areaof square ABCD = 2* triangle DBA = 2 * 1/2 * DB * OA = 288

OA is the radius of the circle and DB is the diameter of the circle. If radius of the circle is r ,

2 r² = 288

r = 12 cm

Area of the shaded part = Area of circle – radius of square

= 3.14 * 12 * 12 – 288 = 164.16 cm²

Meema

thank you! 😊