Q. 154.3( 291 Votes )

# In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Answer :

As quadrant is 1/4 th of a circle and area of circle is Πr^{2}

Area of quadrant =

=154 cm^{2}

Area of triangle=

= 7 × 14

= 98 cm^{2}

In right angle triangle ABC,

BC^{2} = AB^{2} + AC^{2}

BC^{2} = (14)^{2} + (14)^{2}

BC^{2} = 2(14)^{2}

BC= 14 √2 cm

Hence diameter is 14 √2 cm.

Radius is (14 √2)/2 = 7 √2 cm

So, area of the semicircle = 1/2 πr^{2}

= 154 cm^{2}

Area of segment BC = Area of semi-circle - Area of Triangle = 154 - 98 = 56cm

^{2}

Area of the shaded region = Area of semi Circle - Area of segment BC = 154 - 56

= 98 cm^{2}

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Quiz | Area Related with Circles47 mins

Quiz | Imp. Qs. on Circles37 mins

Quiz | Testing Your Knowledge on Circles32 mins

Short Cut Trick to Find Area of Triangle43 mins

Champ Quiz | Area Related with the Circle45 mins

Tricks to MemoriseFREE Class

Trigonometric Identities44 mins

Various Tricks for How to Study Effectively32 mins

Smart and Effective study is the Key of success45 mins

How To Give Dynamic Input to JAVA program?63 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :