Area Calculation

Question

Consider the following set of lines :|x|+|y|=1

Area enclosed by them is

A)1   B)2   C)3    D)4

Comments

It is 2

There are many ways to solve this.

draw the lines , x+y =1, x-y=1,-x+y=1,-x-y =1

1) Then there will be 4 right angle triangle each has hypoteneous as side of a square. Hypo length = root 2.

Hence area = root 2 * root 2

2) Another way is, there will be 2 isosceles triangles will form below and above x axis.

Hence there base is 2 [-1,1], height is 1 area = 1/2 *2 *1 = 1  for each triangle

for two triangles 1+1 =2

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A) 1?

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@ashwin in your second way one isosceles triangle will have area = 1/2

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Nop area will be $\frac{1}{2} * h*b = \frac{1}{2}*1*2 = 1$

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but if we solve with square

each side is 1

So, 1²=1

where is wrong in it?

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Each side is not 1. A side would be hypotenuse of the right angled triangle with sides 1 and 1. By pythagoras, it would be √2

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oh yes , thanks :)

Answer 1

Area= $(\sqrt{2})^{2}$ = 2