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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Naveen

  • Nov 17th, 2005
 

See side of the shaded region, will be a/root(2) and that will be a square too so the area will be a/root(2) *a/root(2) = a^2 /2

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Sheetal Salunkhe

  • Nov 21st, 2005
 

each side of the shaded square will be a/root(2) and  area of square is (side)^2= a/root(2) *a/root(2) = a^2 /2

Sheetal Salunkhe

  • Nov 21st, 2005
 

Area of square is= (side)^2

A=(side)^2

root(A)=each side

by pythagorus law

side of the shaded region will be root(a/2)

then area of the shaded region which is square=a/2

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john

  • Feb 21st, 2006
 

so the aera ="A square"

so the ans =a2/4

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amateur

  • Aug 7th, 2006
 

Ans = A/2

A=a(pow)2

a=root(A)

using Pythagoras Theorm

a' = root(A/2)

therefore a' (pow) 2 = A/2.

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sankalp

  • Mar 27th, 2007
 

ans is a2/2

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jeet_rulzz

  • Aug 22nd, 2008
 

let us assume dat d square is a an unit square ...so d length of d sides of d  sqaure formed by joining d mid points shud b 1/2...so area =1/2*1/2=1/4...
but as told d area of d outer square is a...wat we considered a...so d area of d inner square is a/4.

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keesh

  • Oct 27th, 2009
 

Let the side of outer square A be 2cm

area A=  4sqcm

then side of inner square B= root(2) {by pythagoras law }
area B=2 sqcm which is half of bigger square

B=A/2

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raviaspirant

  • Sep 3rd, 2010
 

Given that all the mid points are joined, this forms a rhombus inside the square whose diagonals are of lenghth equals the side (let 'a') of the square.


And we have area of rhombus = 1/2 (product of diagonals)

Directly we get area of rhombus as 1/2(a^2) == 1/2(area of square)

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