Oxford University MAT 2021 Solved Papers

Question : 1 of 10

Marks: +1, -0

A regular dodecagon is a 12-sided polygon with all sides the same length and all internal angles equal. If I construct a regular dodecagon by connecting 12 equally-spaced points on a circle of radius 1 , then the area of this polygon is

$6+3 √{3}$ ,
$2 √{2}$
$3 √{2}$ ,
$3 √{3}$ ,
3 .

Validate

Solution:

Connect each point to the centre of the circle to split the shape into 12 isosceles triangles, each with angle

30^{∘}

at the centre. Then the area of each triangle is

\;{1}/{2} × 1 × 1 × \sin 30^{∘}=\;{1}/{4}

, and there are 12 triangles, for a total area of 3 .

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