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Q.

Question Image

ABCD is a rectangle inscribed in a circle. What is the area of the shaded region in the above figure if AB = 8cm and BC = 6cm?


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a

29 cm2

b

30.5 cm2

c

25 cm2

d

32.5 cm2  

answer is B.

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Detailed Solution

Given, ABCD is a rectangle inscribed in a circle and AB=8cm and BC=6cm.
Question ImagePythagoras theorem states that the square of the hypotenuse side in a right-angled triangle equals the sum of the squares of the other two sides.
In △ABC, apply pythagoras theorem.
Thus, (AC)2=(AB)2+(AC)2 .
⇒ (AC)2 = 82+62 ⇒ (AC)2 = 100 ⇒ AC=10 .
AC is the diameter of the circle.
Thus, radius=diameter2.
⇒ Radius =AC2
⇒ Radius =102
⇒ Radius =5cm
Area of a rectangle is length×breadth.
⇒ Area of the rectangle ABCD =8×6.
⇒ Area of the rectangle ABCD =48cm2 Area of the circle=πr2.
⇒ Area of the circle =π(5)2 ⇒ Area of the circle =3.14×25 ⇒ Area of the circle =78.5cm2 Thus, the area of the shaded portion = Area of the circle - Area of the rectangle ABCD.
⇒ The area of the shaded portion = (78.5-48)cm2 ⇒ The area of the shaded portion = 30.5cm2
Hence, option 2 is correct.
 
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