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spin [16.1K]
2 years ago
11

. Find the area of the regular dodecagon inscribed in a circle if one vertex is at (3, 0).

Mathematics
1 answer:
devlian [24]2 years ago
4 0

Answer:

Area of the regular dodecagon inscribed in a circle will be 27 square units.

Step-by-step explanation:

A regular dodecagon is the structure has twelve sides and 12 isosceles triangles inscribed in a circle as shown in the figure attached.

Since angle formed at the center by a polygon = \frac{360}{n}

Therefore, angle at the center of a dodecagon = \frac{360}{12} = 30°

Since one of it's vertex is (3, 0) therefore, one side of the triangle formed or radius of the circle = 3 units

Now area of a small triangle = \frac{1}{2}.(a).(b).sin\theta

where a and b are the sides of the triangle and θ is the angle between them.

Now area of the small triangle = \frac{1}{2}.(3).(3).sin30

= \frac{9}{4}

Area of dodecagon = 12×area of the small triangle

= 12×\frac{9}{4}

= 27 unit²

Therefore, area of the regular octagon is 27 square unit.

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