Question

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Answer 1

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Answer 2

Answer: 154.87 cm²

Step-by-step explanation:

Here We have  3  regions

1.) Square ABCD

2.) 4 semi circles:- AED , DHC , CGB , and BFA

3.) Sqaure PQRS

Now,

Side  of square  is  = Diameter of  semi circle

Hence, 14 cm are  divided in 3cm,  radius of circle, side of square , radius  of  circle , 3cm respectively.

If  the  radius  of  circle is r

14 = 3 + r + 2r + r + 3

14 = 6 + 4r

4r = 8

r = 8/4

r = 2 cm

Side of square = 2 × r = 2×2 = 4cm

Area of one  semi circle = πr²/2

Area of 4 semi circle = 4 × πr²/2

Area of 4 semi circle = 2πr² =2π×2×2 = 8π cm²

Area of  square ABCD = 4 × 4 = 16 cm²

Area of square PQRS = 14 × 14 = 196 cm²

Area of shaded region = Area of PQRS - (Area of 4 semi circle + Area of Square ABCD)

Area of shaded region = 196 - (8π + 16)

                                      = 196 - (25.13 + 16 )

                                      = 196 - 41.13

                                      = 154.87 cm²