In figure, ABCD is a trapezium with AB|| DC . AB = 18 cm, DC = 32 cm and distance between AB and DC= 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region of the figure.

Explanation

Given, AB = 18cm, DC = 32 cm, height, (h) = 14cm
and arc of radii = 7 cm
Since, AB || DC
`:. angleA + angleD = 180^(@)`
and `angleB + angleC = 180^(@)`
`:.` Area of sector with angle A and `D = (thetaxxpir^(2))/(360)`
=`(180^(@))/(360)xx(22)/(7)xx(7)^(2)`
= `11xx7 = 77cm^(2)`
similarly, area of sector with angle B and C = 77cm
Now, area of trapezium = `(1)/(2)(AB + DC) xxh`
= `(1)/(2)(18+32)xx14=(50)/(2)xx14= 350cm^(2)`
`:.` Area of shaded region = Area of trapezium - (Area of sector points A and D + Area of sector points B and C)
= `350 - (77+ 77) = 196 cm^(2)`
Hence, the required area of shaded region is `196 cm^(2)` .