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Geometry

Expert replies
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: — Problem Solving |

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.

Image

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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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]
Image
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