n for diagonal lengths p and q, with equality if and only if the diagonals are perpendicular. Let’s work out a few example problems about area of a regular polygon. [40], Of all convex quadrilaterals with given diagonals, the orthodiagonal quadrilateral has the largest area. The area of the four triangles is 4 × ½ × 2 units × 3 units = 12 square units. sin This page describes how to derive the formula for the area of a regular polygon by breaking it down into a set of n isosceles triangles, where n is the number of sides. Lower classes are special cases of higher classes they are connected to. Area of Parallelogram A parallelogram is a 4-sided polygon that has two sets of parallel sides. [46], For a convex quadrilateral ABCD in which E is the point of intersection of the diagonals and F is the point of intersection of the extensions of sides BC and AD, let ω be a circle through E and F which meets CB internally at M and DA internally at N. Let CA meet ω again at L and let DB meet ω again at K. Then there holds: the straight lines NK and ML intersect at point P that is located on the side AB; the straight lines NL and KM intersect at point Q that is located on the side CD. Let each side is of length ‘a’. Find area of the larger circle when radius of the smaller circle and difference in the area is given. Area of Octagon: An octagon is a polygon with eight sides; a polygon being a two-dimensional closed figure made of straight line segments with three or more sides.The word octagon comes from the greek oktágōnon, “eight angles”. For 4 sides with specified lengths and area, I think there are generally 2 discrete possible solutions (one convex and one concave). which is half the magnitude of the cross product of vectors AC and BD. b Regular Polygon case In the case of regular polygons, the formula for the number of triangles in a polygon is: where n is the number of sides (or vertices) . An online calculator calculates a polygon area, given lengths of polygon sides and diagonals, which split polygon to non-overlapping triangles. Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. {\displaystyle B} a Note 1: The most general trapezoids and isosceles trapezoids do not have perpendicular diagonals, but there are infinite numbers of (non-similar) trapezoids and isosceles trapezoids that do have perpendicular diagonals and are not any other named quadrilateral. Find the perimeter of (i) a regular pentagon of side 8 cm (ii) a regular octagon of side 4.5 cm (iii) a regular decagon of side 3.6 cm. This is called the isoperimetric theorem for quadrilaterals. m A quadrilateral is a polygon. A polygon is a ‘n’ sided closed figure.N sided polygon means a polygon with n equal sides. The perpendicular is dividing the side into two parts. 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