Latest Elitmus Aptitude Question SOLUTION: In a square , all the mid points are joined. the inner square is shaded. If the area of the square is A, what is the shaded area?

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(#M40156451) ELITMUS Numerical Ability question Keep an EYE

In a square , all the mid points are joined. the inner square is shaded. If the area of the square is A, what is the shaded area?

Asked In Elitmus divyasree (7 years ago)

Unsolved Read Solution (10)

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amit gadekar  (7 years ago)

the shaded area is half the area of the square (having are A)
therefore answer is A/2

Is this solution Helpfull? Yes (14) | No (3)  

Abhay Tiwari  (7 years ago)

Let the side of the bigger square is 2 units. Then it's Area will be 4 units. Now the smaller square is formed by joining the mid points of the bigger square and after shading the smaller square 4 triangles are left at the corners which are right angles triangle. On applying Pythagoras we can find the side length of the smaller square which will come as (1^{2}+1^{2}=sqrt{2}).

Now the area of the smaller square is (sqrt{2}×sqrt{2}=2)
Which is half of the bigger square.

Is this solution Helpfull? Yes (9) | No (1)  

Himani Gandhi  (7 years ago)

Let the side of square be 'x' so area is x^2= A,
now since the shaded square is formed through mid points, the side of the shaded square would be x/sqrt(2) (Using pythagoras theorem)
hence new area would be (x^2)/2 = A/2

Is this solution Helpfull? Yes (3) | No   

keerthi  (7 years ago)

let, the square side is a. then the area is a*a
the inner sqare side will be a/sqrt(2)
the area of it is a*a/2

Is this solution Helpfull? Yes (1) | No (1)  

ashwini ram  (7 years ago)

if A is the area of the square then rt of A is the side of the square. Then by using Pythagoras theorem, the side of shaded square is sq.rt of (A/2). Therefore the are of shaded square is (A/2)

Is this solution Helpfull? Yes (1) | No   

Avijit  (7 years ago)

This is simple, it is a square, now u r joining mid points so 4 more inner square will be created and each one will have same area which is A/4.

Is this solution Helpfull? Yes (1) | No (1)  

KUMAR HARSH  (7 years ago)

let A=a^2 means side of sqr=a
for inner sqr side=sqrt(a^2/4+a^2/4)=a/sqrt(2)
area of inner=a/sqrt(2)*a/sqrt(2)=a^2/2=A/2

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Amit  (7 years ago)

A/2,
as each side will be of length root(A)/2,
using pythagoras theorem find the side of the shaded square, and hence the area

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PENDYALA SASI SEKHARA VAIBHAV  (7 years ago)

A/2, since shaded area is a2/2

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Digesh Singh Bisht  (1 year ago)

This is a fixed pattern question. In this any square made by joining "mid point" of a square then area of shaded square will always be 1/2 of big square.

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