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?

• the shaded area is half the area of the square (having are A)
  therefore answer is A/2
• 8 years agoHelpfull: Yes(14) No(3)
• 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.
• 8 years agoHelpfull: Yes(9) No(1)
• 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
• 7 years agoHelpfull: Yes(3) No(0)
• 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
• 7 years agoHelpfull: Yes(1) No(1)
• 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)
• 7 years agoHelpfull: Yes(1) No(0)
• 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.
• 7 years agoHelpfull: Yes(1) No(1)
• 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
• 7 years agoHelpfull: Yes(0) No(0)
• 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
• 7 years agoHelpfull: Yes(0) No(0)
• A/2, since shaded area is a2/2
• 7 years agoHelpfull: Yes(0) No(0)
• 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.
• 1 year agoHelpfull: Yes(0) No(0)