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Answer

Radius of the quarter circle = 16/2 – 2= 6 cm

Shaded Area = Area of square – 2 ×Area of a  bigger half circle – Area of quarter smaller circle + 2 × Area of shaded interesection between half bigger circle

Area of shaded interesection between half bigger circle = 2 × ( Area of  quarter bigger half circle – right angle triangle with base and height both 8cm) = 2 × ( 3.14 × 8²/4 – 8²/2) = 36.48 cm²

Shaded Area = 16² – 2 ×3.14 × 8²/2 – 3.14 × 6²/4 + 2 × 36.48  =  99.74 cm²

Note: mr. Tan has the better solution!

 

 

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my child has similar question and both of your answers help a lot. thanks!

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The leave-shaped portion can be split and moved.
Then we have an isosceles right angle triangle width side 16cm
minus a quadrant of radius 16/2 - 2 = 6cm.

Shaded area is 16 x 16 / 2 - pi x 6 x 6 / 4 = 99.74 cm2.
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