a regular octagon is formed by cutting congruent isoceles traingles from the corners of a square,if the square has side length 1 the side length of the octagon is?

kvpy ques

Question

a regular octagon is formed by cutting congruent isoceles
traingles from the corners of a square,if the square has side
length 1 the side length of the octagon is?
kvpy ques

Ajanta Trivedi · Accepted Answer

ABCD is a square of side length 1 isosceles triangles are cut from the corners let AP = x , in the right angled triangle PAW; $P W^{2} = A P^{2} + A W^{2} = x^{2} + x^{2} = 2 x^{2} P W = \sqrt{2} x$ WV = 1- (x+x) = 1-2x since PQRSTUVW is a regular octagon therefore PW = WV $\sqrt{2} x = 1 - 2 x (2 + \sqrt{2}) x = 1 x = \frac{1}{2 + \sqrt{2}} = \frac{1}{2 + \sqrt{2}} * \frac{2 - \sqrt{2}}{2 - \sqrt{2}} = \frac{2 - \sqrt{2}}{4 - 2} = \frac{2 - \sqrt{2}}{2}$ thus side length of octagon is $\sqrt{2} x = \sqrt{2} * \frac{2 - \sqrt{2}}{2} = \sqrt{2} - 1$ units hope this helps you cheers!!

a regular octagon is formed by cutting congruent isoceles traingles from the corners of a square,if the square has side length 1 the side length of the octagon is? kvpy ques

a regular octagon is formed by cutting congruent isoceles traingles from the corners of a square,if the square has side length 1 the side length of the octagon is?

kvpy ques