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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 FACT
Consider the blue square in the left diagram. It has side 2x and
so its area is 4x2. The pink square in the middle is half of the
blue one so its area is 2x2. Rotating it 45 degrees to get the
right diagram. It tells us that if a square has area 2x2, 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 122 = 288 cm2, 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 122 - 288 = 164.16 cm2.

The FUN FACT is often useful in competitions.

 

 

1 Reply 2 Likes ✔Accepted Answer

Thank you! So much clearer now👍🏻😁

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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

 

1 Reply 2 Likes

thank you! 😊

0 Replies 0 Likes