Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
803 views
in Co-ordinate geometry by (60 points)
edited by

A square with side 'a' is revolved about its centre through 45°. What is the area common to both the squares?

a) 2(√2-1)a2

b) (√2+1) a2/2

c) (√3-1) a2

d) (√5-1) a2

Please log in or register to answer this question.

1 Answer

0 votes
by (44.1k points)

Common area = Area of Δ ACD - 2 x Area of Δ CDE

 = \(\frac{a^2}2-2\times\frac12\times cd^2\) 

 = \(\frac{a^2}2-(OC-OD)^2\) 

 = \(\frac{a^2}2-(\frac a{\sqrt2}-\frac a2)^2\) 

 = \(\frac{a^2}2-\frac{a^2}2(1-\frac 1{\sqrt2})^2\) 

 = \(\frac{a^2}2-(1-(1+\frac12-\frac2{\sqrt2}))\) 

 = \(\frac{a^2}2-(\sqrt2-\frac12)\) 

 = \(\frac{a^2}4(2\sqrt2-1)\) square units.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...