Combination of quadrilateral and circle : In Figure; ABCD is a trapezium with AB||DC ; AB = 18cm; DC = 32cm and the distance between AB and DC is 14 cm. Circles 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

Area of shaded region = area of trapezium `-` area of four sectors
`(1)/(2) xx 14(32 + 18) - [pi (7)^(2) xx (angleA)/(360^(@)) + pi (7)^(2) xx (angle B)/(360^(@)) + pi (7)^(2) xx (angleC)/(360^(@)) + pi (7)^(2) xx (angleD)/(360^(@))]`
`= 7 xx 50 - (pi xx (7)^(2))/(360^(@)) (angle A + angle B + angle C + angle D)`
`= 350 - (22)/(7) xx (7 xx 7)/(360^(@)) xx 360^(@)` ( `:'` sum of the four angles of a quad, is `360^(@)`)
`= 350 - 154 = 196 cm^(2)`
Hence, area of shaded region is `196 cm^(2)`