Geometry

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Sun Feb 07, 2010 7:26 am

The area confined between the graphs |x| = |y| and |x| = a is

(A)2(a^2)
(B)4(a^2)
(C)(a^2)
(D)(a^2)/2
(E)None of the above.

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Source: Beat The GMAT — Problem Solving | Sun Feb 07, 2010 7:26 am

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sun Feb 07, 2010 7:29 am

harsh.champ wrote:The area confined between the graphs |x| = |y| and |x| = a is

(A)2(a^2)
(B)4(a^2)
(C)(a^2)
(D)(a^2)/2
(E)None of the above.

|x|=a --> x=+/-a
and |x| = |y| --> x = +/-y

so we can make a raph of following equations.

Now from graph we have to calculate the area of shaded section..
The area of this section is half of the area of square = ((2a)^2)/2

Ans is [spoiler](A)2(a^2)[/spoiler]

Last edited by shashank.ism on Sun Feb 07, 2010 8:40 am, edited 4 times in total.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sun Feb 07, 2010 7:43 am

harsh.champ wrote:The area confined between the graphs |x| = |y| and |x| = a is

(A)2(a^2)
(B)4(a^2)
(C)(a^2)
(D)(a^2)/2
(E)None of the above.

The area of 1 triangle = 1/2 *base*height = 1/2*2a*a = a^2 [refer the pic]
Total area = 2*a^2
[spoiler]
A[/spoiler]

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