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
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