Q26 of 45 Page 12

In figure 3, ABCD is a trapezium of area 24.5 cm2. In it, AD || BC, ∠DAB = 90°, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region. [Use π = 22/7

(CBSE 2014)

Area of trapezium = × (sum of parallel sides) × height

⇒ 24.5 = × (10 + 4) × AB


⇒ 49 = 14 × AB


⸫ AB = cm


⸫ Radius of the quadrant of the circle = AB = cm


Area of the quadrant =


=


= = 9.625 cm2


⸫ Area of the shaded region = Area of the trapezium – Area of the quadrant


= 24.5 – 9.625 cm2


= 14.875 cm2

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