Question

Q. In the given figure, If AOB is diameter, then the area of shaded region is:
(a) 61 cm square
(b) 532 cm square
(c) 147 cm square
(d) 227 cm square
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Answer 1

Answer:

In Fig., OACB is a quadrant of a circle with centre O and radius 3.5 cm . If OD = 2 cm , find the area of the(i) 

Answer 2

61 cm²

Given:

AC= 12 cm , AB= 16 cm AB is diameter

Therefore

∠ACB = 90° (angles in a semicircle are right angle)

∴ ΔACB is a right angle triangle right angled at C

Using Pythagoras theorem:

The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.

H^2= P^2+B^2

where H is hypotenuse

, P is perpendicular and B is base

\Rightarrow AB^2=12^2+16^2\\\Rightarrow AB^2= 400\\\Rightarrow AB=\sqrt{400} =20

Now as we know area of semi-circle is given by area=\dfrac{\pi r^2}{2}

where r is radius of circle and area of triangle is given by area= \dfrac{1}{2} \times base\times height

Now r= 10 cm ,

base=12cm

and height = 16cm

Area of shaded region = area of semicircle- area of triangle

= \dfrac{\pi \times 10^2}{2} -\dfrac{1}{2} \times 12\times 16\\\\=\dfrac{22 \times 100}{7\times 2} - 6 \times 16\\\\=157.14-96=61.14cm^2

Hence area of shaded region is 61.14 cm²

$\color{blue}{ Answered \ by \ Srijan}$