CLEAR
Toprankers-Info

+91 7676564400

Mobile App

Get it on Google Play
Discussions
Select Date
Tags:

Articles

Discussions
Submit Discussion
KS

· started a discussion

· 1 Months ago

Doubt? (Question:107680.0)

Is the triangle an equilateral one?

Question:

In the adjoining figure ACB is a quadrant with radius ‘a’. A semicircle is drawn outside the quadrant taking AB as a diameter. Find the area of shaded region:



Options:
A) \(\cfrac{1}{4}(\pi -2a^2)\)
B) \(\cfrac{1}{4}(\pi a^2 -a^2)\)
C) \(\cfrac{a^2}{2}\)
D) Can’t be determined
Solution:
Ans: (c)

 In triangle ABC by PGT

\(AB^2=AC^2+BC^2\) 

\(AB^2=a^2+a^2 = 2a^2 \)
\(AB=a\sqrt{2}\)

Area of shaded region = Area of semicircle - (Area of sector ACB - Area of \(\triangle\)ABC)

\(=\cfrac{1}{2}\pi \cfrac{a^2}{2}-\left ( \cfrac {1}{4}\pi a^2-\cfrac{1}{2}a^2 \right )\)

\(=\cfrac{\pi a^2}{4}-\cfrac{\pi a^2}{4}+\cfrac{1}{2}a^2=\cfrac{1}{2}a^2\)

Abhishek Shrivastava

· commented

· 1 Months ago

Dear Student

Given answer is correct and given triangle is a Right angle triangle
keep learning with us

Regards
Team TR
-logo
We at aim to provide most comprehensive content & test for practice which is carefully divided into various chapters and topics to help you focus on your weak areas.Our Practice mock test gives you unmatched analytics to help you realize your strong areas,time management and improvement areas.Our Short & Crisp notes on each topic will help you to quickly revise the topic along with the tips & tricks of the exams.
More About
-Info
-Info

Mobile App

Get it on Google Play
About Us Campus Ambassador Careers Contact Us Refund Policy

All Rights Reserved Top Rankers

User Policy
Disclaimer
Terms & Conditions