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  • In Figure, ABCD is a trapezium with AB parallel DC, AB equal to 18 cm, DC equal to 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.

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.

Answers (1)

 [196 m2]

Solution

Given  AB = 18 cm

DC = 32 cm

Radius of circle = 7 cm

Area of trapezium =\frac{1}{2} ×  sum of the parallel sides distance between parallel sides.

                        = \frac{1}{2} ×(AB+CD) × 14

                        =\frac{1}{2} ×(18+32) × 14

                        =(50) × 7

                        =350 cm2

\theta=\angle A+\angle B+\angle C+\angle D  = 360°                   (sum of interior angles of quadrilateral)

Radius = 7 cm

Area of all sectors =\frac{\theta}{360^{\circ}}\times \pi r^{2}       here \theta=360^{\circ}

                              =\pi r^{2}

                             =\frac{22}{7}\times 7 \times 7

                             =154 cm2

Area of shaded region = Area of trapezium – Area of all sectors

                                   =350-154=196 cm2

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