UKMT Special (Problem $20$ )

The diagram shows a regular dodecagon and a square, whose vertices are also vertices of the dodecagon.

Find the value of the ratio

area of square: area of dodecagon

[UKMT Hamilton Olympiad $2018$ , H $3$ ]

#Geometry

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

You have until next Saturday, $3:00$ pm!

Yajat Shamji - 6 months, 3 weeks ago

This is the method I used to solve it, then when I checked the solutions for UKMT, it seems my method and answer were correct, so instead of wasting my time to write a solution, I'll just post a pic here.

Solution -

Troll Solution, because there is no solution

A Former Brilliant Member - 6 months, 2 weeks ago

I'm the one that's supposed to post the official solution, not you!

Yajat Shamji - 6 months, 2 weeks ago

lol ok, I'll delete it :P

A Former Brilliant Member - 6 months, 2 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

UKMT Special (Problem 202020)

Comments

UKMT Special (Problem $20$ )