Regular Octagon Made By Cutting Equal Triangles Out From The Corners Of A Square Date of Exam May 2018 Subject Mathematics, Surveying and Transportation Engineering 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 Click here to show or hide the Answer Key Answer: [ A ] Solution Click here to expand or collapse this section $x^2 = a^2 + a^2$ $x^2 = 2a^2$ $x = \sqrt{2}a$ $x + 2a = 16$ $\sqrt{2}a + 2a =16$ $\left( \sqrt{2} + 2 \right)a = 16$ $a = \dfrac{16}{\sqrt{2} + 2}$ $x = \sqrt{2}\left( \dfrac{16}{\sqrt{2} + 2} \right)$ $x = 6.627 ~ \text{cm}$ ← answer Category Plane Geometry Regular Octagon Regular Polygon Log in or register to post comments
