10/7/2023 0 Comments Plane and solid geometry formulas![]() Square c a 4Aquad Sector of a circle Area = ½ r2 radians = C b Circles 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 sides b ra = A T rc = A T rb = A T s a s c s b s = ½(a + b + c + d) r Note: 1 radian is the angle such that C = r. The following are some names of polygons. O r = angle in radians 6 (s a)(s b)(s c)(s d) Circle incribed in a quadrilateral b Area = Asector – Atriangle Area = ½ r2 r – ½ r2 sin Area = ½ r2 (r – sin ) r 6 r c a D Segment of a circle Parabolic segment Polygons are classified according to the number of sides. bh h Ellipse b Area = a b Perimeter, P P = 2 r= Aquad = O Area = Asector + Atriangle Area = ½ r2 r + ½ r2 sin Area = ½ r2 (r + sin ) Area = A circle is inscribed in a quadrilateral if it is tangent to the three sides of the quadrilateral. b d (ab cd)(ac bd)(ad bc) r 180 C 2 r 360 r r triangle quadrangle or quadrilateral pentagon hexagon heptagon or septagon octagon nonagon C r 2 3 r a Aquad s c d s = ½(a + b + c + d) abcd SOLID GEOMETRY = 360 - r r POLYHEDRONS A polyhedron is a closed solid whose faces are polygons. ![]() 4 a a Diagonal, d = a 2 General quadrilateral C b d1 2 d2 d Given diagonals d1 and d2 and included angle : A = ½ d1 d2 sin 5 3 c D A 4 3 B 2 1 1 5 = Circle 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. Circumscribing x circle A = ab sin A C A B a 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 h b c d1 d2 D Area = d A A + C = 180° B + D = 180° Area = ½ C r POLYGONS d Area, A = a2 Perimeter, P = 4a There are two basic types of polygons, a convex and a concave polygon. 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. (s a)(s b)(s c)(s d) abcdcos2 A= Tacloban City s= a b c d 2 = A C B D or = 2 2 A = ½ ab sin B + ½ cd sin D 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. ![]() Prepared by: RTFVerterra Plane and Solid Geometry Formulas ASIAN DEVELOPMENT FOUNDATION COLLEGE Given four sides a, b, c, d, and sum of two opposite angles: The content of this material is one of the intellectual properties of Engr.
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