![]() Number of diagonals, D The diagonal of a polygon is the line segment joining two non-adjacent sides. Given three sides a, b, and c: (Hero’s Formula) A = s(s a)(s b)(s c)Ī circle is circumscribed about a triangle if it passes through the vertices of the triangle.ĭ a Given diagonals d1 and d2 and included angle : A = ½ d1 d2 sin Ĭircle circumscribed about a triangle (Cicumcircle) Given two sides a and b and included angle : A = ½ ab sin The area under this condition can also be solved by finding one angle using cosine law and apply the formula for two sides and included angle. X = side = angle subtended by the side from the center R = radius of circumscribing circle r = radius of inscribed circle, also called the apothem n = number of sidesĬyclic Quadrilateral A cyclic quadrilateral is a B quadrilateral whose vertices lie on the circumference ofĪpply the formula for two sides and included angle. = 360° / n Area, A = ½ R2 sin n = ½ x r nĬircle inscribed in a triangle (Incircle) A circle is inscribed in a triangle if it is tangent to the three sides of the triangle. Perimeter, P = n x n 2 Interior angle = n 180° “For any cyclic quadrilateral, the product of the diagonals equals the sum of the products of the opposite sides” d1 d2 = ac + bd Note: 1 radian is the angle such that C = r.Ĭircles escribed about a triangle (Excircles) A circle is escribed about a triangle if it is tangent to one side and to the prolongation of the other two sides. 3 sides 4 sides 5 sides 6 sides 7 sides 8 sides 9 sidesī ra = A T rc = A T rb = A T s a s c s b The following are some names of polygons. ![]() Polygons are classified according to the number of sides. POLYHEDRONS A polyhedron is a closed solid whose faces are polygons.Īrea = Asector + Atriangle Area = ½ r2 r + ½ r2 sin Area = ½ r2 (r + sin )Ī circle is inscribed in a quadrilateral if it is tangent to the three sides of the quadrilateral.Īrea = Asector – Atriangle Area = ½ r2 r – ½ r2 sin Area = ½ r2 (r – sin ) r Triangle quadrangle or quadrilateral pentagon hexagon heptagon or septagon octagon nonagon Given diagonals d1 and d2 and included angle : A = ½ d1 d2 sin Ĭircle circumscribed about a quadrilateral A circle is circumscribed about a quadrilateral if it passes through the vertices of the quadrilateral. The following figure is a convex polygon. A convex polygon is one in which no side, when extended, will pass inside the polygon, otherwise it called concave polygon. There are two basic types of polygons, a convex and a concave polygon. Given three angles A, B, and C and one side a: a 2 sinB sinC A= 2 sin A The area under this condition can also be solved by finding one side using sine law and The area of a regular polygon can be found by considering one segment, which has the form of an isosceles triangle. Polygons that are both equilateral and equiangular are called regular polygons. Polygons with equal interior angles are called equiangular polygons. Polygons whose sides are equal are called equilateral polygons. ![]() Reproduction of this copyrighted material without consent of the author is punishable by law. Verterra of Asian Development Foundation College. The content of this material is one of the intellectual properties of Engr. Given four sides a, b, c, d, and sum of two opposite angles: Plane and Solid Geometry Formulas ASIAN DEVELOPMENT FOUNDATION COLLEGE ![]()
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