Area of shaded region = area of bigger square - area of unshaded region

area of unshaded region = area of four semi circle + area of the inner square

Area of shaded region = Area of rectangle - Area of 6 semicircles

Given length of the rectangle = 21cm

Diameter of each semi circle = \\(\\frac{21}{3}\\)

Area of shaded region = Area of square MNOP - Area of four circles

Area of shaded region = 80/360 x 3.14x 10x 10 - 80/360 x 3.14 x 7x7

Area of shaded region = Area of quadrant - Area of the square

To find the radius of quadrant use pythagoras theorem

\\(OQ^{2}= PQ^{2}+OP^{2}\\)

Area of the shaded region PQRS = Area of OPQ – Area of the ORS

Area of shaded region = Area of the rectangle - Area of triangle

step 1- Find the Area of square and Area of quadrant

step 2- Area of 4 quadrant

step 3- Area of shaded region = Area of square - Area of quadrant

Area of shaded region = Area of square - Area of 4 circle

Area of triangle = 78 cm^{2}

Area of circle = 3.14 x 8 x8

From the area of circle subtract the area of quadrant with angle = \\(60^\\circ\\)

Now , add the area of triangle with the resultant to get the answer of shaded region.