# GEOMETRY_Formulas.pdf - Nature of GEOMETRY Mathematics in...

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Nature of GEOMETRY Mathematics in the Modern World /mvcv 2018

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Plane Geometry FORMULAS
Recall fundamental theorems of: A. Angles B. Parallel Lines C. Triangle D. Quadrilateral E. General polygon F. Circles

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TRIANGLES P = a + b + c A = 1 2 ?ℎ A = 1 2 ? 𝑃 A = ?(? − ?)(? − ?)(? − ?) Where: P = perimeter a, b, c = sides A = area b = base h = altitude r = apothem, radius of inscribed circle s = semi-perimeter ? = 1 2 (? + ? + ?) 𝜃 = included angle ? = 1 2 ? ? ?𝑖?𝜃 a b c
RIGHT TRIANGLE ? 2 = ? 2 + ? 2 A = 1 2 ? ?

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Equilateral Triangle 𝑃 = 3? ℎ = 3 2 ? A = 3 4 ? 2 ? = 3 6 ? ? = 2 3 ℎ = 3 3 ? ? = 3 ?
QUADRILATERALS RECTANGLE A = a b P = 2 (a + b) Diagonal, ? = ? 2 + ? 2 d SQUARE a a ? = ? 2 𝑃 = 4? Diagonal, ? = ? 2

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QUADRILATERALS PARALLELOGRAM A B C D ? 1 ? 2 h a b P = 2(a+b) ? = ?ℎ ? = 1 2 ? 1 ? 2 sin 𝜃 𝜃
QUADRILATERALS RHOMBUS a a h A = ah P = 4a ? = 1 2 ? 1 ? 2 ? 2 = 1 2 ? 1 2 + 1 2 ? 2 2 a a ? 1 ? 2 Where: ? 1 = ???𝑔?? ?𝑖?𝑔???? ? 2 = ?ℎ????? ?𝑖?𝑔????

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QUADRILATERALS TRAPEZOID a b h ? = 1 2 ? + ? ℎ ? = ? ℎ Where: m = median
GENERAL POLYGON ? = 1 2 ? 𝑃 Where: r = radius of the inscribed circle P = perimeter Regular Polygon (both equilateral and equiangular) A = 1 2 ? 𝑃 ? = 1 2 ???

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