# Regular Octagon Made By Cutting Equal Triangles Out From The Corners Of A Square

Date of Exam:

**Problem**

A regular octagon is made by cutting equal isosceles right triangles out from the corners of a square of sides 16 cm. What is the length of the sides of the octagon?

A. 6.627 cm | C. 6.762 cm |

B. 6.267 cm | D. 6.276 cm |

**Answer Key**

Answer: [ A ]

**Solution**

$x^2 = a^2 + a^2$

$x^2 = 2a^2$

$x = \sqrt{2}a$

$x + 2a = 16$

$\sqrt{2}a + 2a =16$

$\left( \sqrt{2} + 2 \right)a = 16$

$a = \dfrac{16}{\sqrt{2} + 2}$

$x = \sqrt{2}\left( \dfrac{16}{\sqrt{2} + 2} \right)$

$x = 6.627 ~ \text{cm}$ ← *answer*

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