If n is large, then 2 Pi /n is very small and sin (2 pi/n) may be approximated by 2 pi / n so that the area may be approximated byįor more on the above question, see the interactive tutorial in regular polygons.The area of a regular polygon with n sides may be given in terms of R by.(HINT: If angle x is very small and is in radians, then sin x may be approximated by x). Show that if the number of sides n of a polygon inscribed inside a circle of radius R, is very large then the area of the polygon may be approximated by the area of the circumscribed circle with radius R. = 403.1 mm 2 (approximated to 1 decimal place). We now use the formula for the area when the side of the regular polygon is knownĪrea = (1 / 4) (12) (6 mm) 2 cot (180 o / 12).A dodecagon is a regular polygon with 12 sides and the central angle t opposite one side of the polygon is given by.(approximate your answer to one decimal place). Side of pentagon = 2 OM tan(t / 2) = 8.7 cm (answer rounded to two decimal places)įind the area of a dodecagon of side 6 mm. The side of the pentagon is twice MB, hence.OM is the radius of the inscribed circle and is equal to 6 cm. The theorem of Pythagoras states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. For this section, the following are accepted as axioms. Let M be the midpoint of AB so that OM is perpendicular to AB. An axiom is an established or accepted principle. HenceĪ circle of radius 6 cm is inscribed in a 5 sided regular polygon (pentagon), find the length of one side of the pentagon.(approximate your answer to two decimal places). So all three angles of the triangle are equal and therefore it is an equilateral triangle.Since OA = OB = 10 cm, triangle OAB is isosceles which gives Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end.Regular polygons problems with detailed solutions.Ī 6 sided regular polygon (hexagon) is inscribed in a circle of radius 10 cm, find the length of one side of the hexagon.
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