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In Fig. 11.17, 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

In Fig. 11.17, 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

Solution:

Given, ABCD is a trapezium with sides

AB = 18 cm

DC = 32 cm

The distance between AB and DC = 14 cm

Also, AB||DC

Radii of arcs with centres A, B, C and D = 7 cm

We have to find the area of the shaded region.

Area of the shaded region = area of trapezium - area of 4 sectors.

since AB||DC,  ∠A + ∠D = 180° and ∠B + ∠C = 180°

Area of sector = πr²θ/360°

Area of sectors with angles A and D = π(7)²[(∠A+∠D)/360°]

= 49π(180°/360°)

= 49π(1/2)

= 49(22/7)(1/2)

= 7(11)

= 77 cm²

Area of sectors with angles B and C = π(7)²[(∠B+∠C)/360°]

= 49π(180°/360°)

= 49π(1/2)

= 49(22/7)(1/2)

= 7(11)

= 77 cm²

Area of 4 sectors = 77 + 77

= 154 cm²

Area of trapezium = 1/2[(sum of parallel sides) × height]

From the figure,

The parallel sides are AB and CD

Given, AB = 18 cm and CD = 32 cm

Height = distance between AB and CD

So, height = 14 cm

Now, the area of trapezium = 1/2[(18 + 32) × 14]

= 1/2[(50) × 14]

= 1/2(700)

= 350 cm²

Area of shaded region = 350 - 154

= 196 cm²

Therefore, the area of the shaded region is 196 cm²

✦ Try This: Adjoining fig, ABCD is a trapezium with AB ll DC and ∠ BCD = 30° Fig. BGEC is a sector of a circle with centre C and AB = BC = 7,cm DE = 4 and BF = 3.5 cm, then find the the area of the shaded region.(Useπ =22/7)

Adjoining fig, ABCD is a trapezium with AB ll DC and ∠ BCD = 30° Fig. BGEC is a sector of a circle with centre C and AB = BC = 7,cm DE = 4 and BF = 3.5 cm, then find the the area of the shaded region.(Useπ =22/7)

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 6

In Fig. 11.17, 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

Summary:

In Fig. 11.17, 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 the area of the shaded region of the figure is 196 cm²

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