Question

find the area of the shaded region​

Answer 1

Look well. There is a square inside the unshaded region.

If you connect the points.

There will be a semicircle in each side of the square.

If the side of the square is X cm

Then the Radius of the semi circle is X/2

As the total length of side of big square is 14 cm and with given 3cm on both sides. We can tell the length of the shape inside is 8cm

Which means X + x/2 +X/2= 8 cm

2x = 8 cm

x = 4 cm

Area of the small sq. is =

${4}^{2}$

=16 cm sq.

Area of the four semi circles =

$4 \times \frac{\pi {r}^{2} }{2}$

$2\pi {r}^{2}$

$2 \times \frac{22}{7} \times {2}^{2}$

= 25.14 cm sq.

Area of the unshaded region = 31.14 cm sq. units

Area of the big square =

${14}^{2}$

=196 cm sq.

Area of the shaded region = 196 - 31.14

Answer = 164.86 cm sq.