Question

a square whose sides are 2 cm,have got its corners cut.a regular octagon is formed find the length of each side

Answer 1

Each side is 16cm.
Hope this will help.

Answer 2

Let ABCd is a square and AB = BC = CD=  DA = 2 m

Again, we form a rectangular octagon by cutting all four corners.

Let EF = FG = GH = HI = IJ = JK = KL = LE = x

Now, by symmetry, we get

AE = Al = BG = BF = Ch = CI = DJ = Dk = a

In triangle ALE, apply Pythagorus theorem,

      AL2 = AE2 + LE2

=> x2 = a2 + a2

=> x2 = 2a2

=> x = a√2

=> a = x/√2 ....................1

Again, AB = AE + EF + FB

=> 2 = a + x + a

=> 2 = 2a + x

=> 2 = 2x/√2 + x

=> √2x + x = 2

=> (√2 + 1)x = 2

=> x = 2/(√2 + 1)

So, the side of an octagon is 2/(√2 + 1) m