Question

Find the area of the shaded part in the figure. (Use π=3.14)

Answer 1

Given :

A rectangle with sides 12cm and 5cm is enclosed in a circle

To find :

Area of the shaded region

Explanation:

The area of the traingle ABCD :

= Length × breath

= 5cm × 12cm

= 60cm^2

Now the radius of the circle :

(Using phytagoras theorem)

$ac {}^{2} = ad {}^{2} + dc {}^{2} \\ ac {}^{2} = (5cm) {}^{2} + (12cm) {}^{2} \\ ac {}^{2} = 25cm {}^{2} + 144cm { }^{2} \\ ac {}^{2} = 169cm {}^{2} \\ ac = \sqrt{169cm {}^{2} } \\ ac = 13cm$

AC = Diameter

hence Radius = D/2 = 13cm/2

Area of the circle :

$= \pi \: r {}^{2} \\ = \frac{22}{7} \times ( \frac{13}{2} )( \frac{13}{2} ) \times cm {}^{2} \\ = 133cm {}^{2}$

Area of the Shaded region = Area of the circle - area of the rectangle ABCD

$= 133cm {}^{2} - 60cm {}^{2} \\ = 73cm {}^{2}$

Answer 2

Answer:

Area of Shaded Region=72.665 cm²

Step-by-step explanation:

From the Figure:-

AC is the diagonal of Rectangle ABCD and diameter of the circle too.

To Find:-

The area of the shaded region.

Formula Applied:-

Area of circle=πr²

Area of Rectangle= length×breadth

Solution:-

In ΔADC,

Applying Pythagoras Theorem,

H²=P²+B²

(AC)²=(5)²+(12)²

(AC)²=25+144

(AC)²=169

AC=$\sqrt{169}$

AC= 13 cm

According to the given Figure:-

Area of Shaded Region=Area of Circle-Area of Rectangle

Area of Shaded Region=πr²-(l×b)

Radius of the circle=$\frac{AC}{2}$=$\frac{13}{2}$cm

Area of Shaded Region=(3.14×$\frac{13}{2}$×$\frac{13}{2}$)-(5×12)

Area of Shaded Region=132.665-60

Area of Shaded Region=72.665 cm²