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?

Answer Key

Solution

$x^2 = 2a^2$

$x = \sqrt{2}a$

$x + 2a = 16$

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

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

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

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

$x = 6.627 ~ \text{cm}$ ← answer

MATHalino