Given-
ABCD is a trapezium. AB∥DC and AB=18 cm, DC=32 cm.
There are 4 arcs centring the vertices A,B,C,D with radius r=7 cm.
To find out - area of shaded region
Solution-
Area of trapezium =12× sum of the parallel sides × distance between the parallel sides.=12×(AB+CD)×14=12×(18+32)×14cm2=350 cm2.
Let us take the angles of the trapezium as a at A,b at B,c at C and d at D.
Now the given arcs form 4 sectors.
Together they form a circle of radius r=7 cm as a+b+c+d=360o.
∴ The area of the sectors=area of circle with radius (r=7cm) =π×r2=227×72=154 cm2.
∴ Area of shaded region = area of trapezium − area of circle
=(350−154)=196 cm2.