Areas - Table of Content

81.

Proposed Problem 174. Quadrilateral with Midpoints, Triangles, Areas.  

80.

Proposed Problem 173. Quadrilateral with Midpoints, Triangles, Areas.  

79.

Proposed Problem 172. Trapezoid, Midpoints, Quadrilaterals, Areas.  

78.

Proposed Problem 171. Trapezoid, Midpoints, Triangles, Areas.  

77.

Proposed Problem 170. Trapezoid, Midpoint, Triangle, Area.  

76.

Proposed Problem 169. Parallelogram, Interior and Exterior Points, Diagonals, Pentagon, Triangles, Areas  

75.

Proposed Problem 168. Parallelogram, Diagonal, Triangles, Pentagon, Areas.  

74.

Proposed Problem 167. Parallelogram, Diagonal, Triangles, Areas.  

73.

Proposed Problem 166. Parallelogram, Diagonal, Triangles, Areas.  

72.

Proposed Problem 165. Parallelogram, Diagonal, Triangles, Areas.  

71.

Proposed Problem 164. Parallelogram, Trapezoid, Diagonal, Triangles, Areas.  

70.

Proposed Problem 163. Trapezoid, Diagonals, Triangles, Areas.  

69.

Proposed Problem 162. Parallelogram, Triangles, Areas.  

68.

Proposed Problem 161. Parallelogram, Midpoints, Octagon, Areas.  

67.

Proposed Problem 151. Quadrilateral, Area, Trisection of Sides.  

66.

Proposed Problem 150. Quadrilateral, Area, Trisection of Sides.  

65.

Proposed Problem 149. Quadrilateral, Area, Midpoints.  

64.

Proposed Problem 148. Quadrilateral, Area, Midpoints.  

63.

Proposed Problem 147. Quadrilateral, Area, Midpoints, Triangle.  

62.

Proposed Problem 146. Varignon's Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter.  

61.

Proposed Problem 142. Four Triangles, Incircle, Tangent and Parallel to Side, Areas.  

60.

Proposed Problem 139. Triangle Area, Orthic Triangle, Semiperimeter, Circumradius.  

59.

Right Triangles, Formulas and Facts
Pythagorean theorem, Similarity, Geometric mean, hypotenuse, legs, semiperimeter, altitude, median, similar shapes areas, centers, orthocenter, incenter, centroid, circumcenter, radius, inradius, circumradius, exradius, circles, incircle, circumcircle, excircle.

58.

Pythagorean Theorem, 47th Proposition of Euclid's Book I, Video.

57.

Heron's Formula.
Key facts and a purely geometric step-by-step proof.
 

56.

Heron's Formula with medians 

55.

Kurschak's Tile and Theorem. Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric way of finding the area of a regular dodecagon.
 

54.

Archimedes' Book of Lemmas. Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve these 15 high school level problems and lift up your geometry skills.
 
Proposition 4 Arbelos

53.

Archimedes Proposition 7. Circles and Squares

52.

Proposition 14 area of the Salinon.

51.

Brahmagupta's Formula  Area of a cyclic quadrilateral.

50.

Brahmagupta Formula Extension Area of any quadrilateral.

49.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions.

48.

Hippocrates and Squaring the Circle
 

47.

Lunes of Hippocrates 4
 

46.

Lunes of Hippocrates 3
 

45.

Lunes of Hippocrates 2
 

44.

Lunes of Hippocrates 1
 

43.

Pythagoras and Circle Area
 

42.

De Gua's Theorem

41.

Triangle and Squares 22
 

40.

Triangle and Squares 21
See also: Triangle and Squares 19

39.

Triangle and Squares 20

38.

Triangle and Squares 19  

37.

Triangle and Squares 18  Sangaku Problem

36.

Cyclic Quadrilateral: Ratio of the Diagonals
 

35.

Ptolemy's Theorem.
 

34.

Marion Walter's Theorem: Triangle and Hexagon areas: Using TracenPoche Dynamic Geometry Software

33.

Proposed Problem 125. Area of Triangle, Star, Trisection of Sides.

32.

Proposed Problem 124. Area of triangle, Similarity, Trisection of Sides.

31.

Proposed Problem 123. Area of triangle, Similarity, Trisection of Sides.

30.

Proposed Problem 122. Marion Walter's Theorem. Area of triangle and Hexagon, Trisection of Sides.

29.

Proposed Problem 121. Similarity and Area of triangle, Trisection of Sides.

28.

Proposed Problem 120. Area of triangle, incenter, excircles, tangent.

27.

Proposed Problem 119. Area of triangle, incenter, excircle, tangent.

26.

Proposed Problem 118. Area of triangle, incenter, excenter, tangent.

25.

Proposed Problem 117. Area of triangle, incenter, excircles, tangent.

24.

Proposed Problem 116. Area of triangle, excircles, tangent.

23.

Proposed Problem 115. Area of triangle, excircles, tangent.

22.

Proposed Problem 114. Area of triangle, incircle, excircle.

21.

Proposed Problem 113. Area of triangle, incircle, excircle.

20.

Proposed Problem 112. Area of square and triangle.

519.

Proposed Problem 110. Area of Contact Triangle.

18.

Proposed Problem 103.Equilateral Triangle Area, Interior Point, Heron's Formula.

17.

Proposed Problem 102.Equilateral Triangle Area, Interior Point.

16.

Proposed Problem 100. Circle Area, Archimedes' Book of Lemmas.

15.

Proposed Problem 99: Circle Area, General Extension to Pythagoras' Theorem.

14.

Proposed Problem 98. Quadrilateral Area, Centroid, Similarity.

13.

Proposed Problem 97. Similar Triangles, Areas.

12.

Proposed Problem 90. Quadrilateral and Triangle Areas, Midpoints.

11.

Proposed Problem 89. Triangles of equal area, Midpoints.

10.

Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints.

9.

Proposed Problem 87. Area of Quadrilaterals and Midpoints of Diagonals.

8.

Proposed Problem 86. Intouch and Extouch Triangles, Areas.

7.

Proposed Problem 85. Contact Triangles Areas, Incircle, Excircle.

6.

Proposed Problem 84. Contact Triangles Areas, Incircle, Excircle, Inradius, Exradius.

5.

Proposed Problem 83. Area of the Excircle Contact Triangle, exradius, circumradius.

4.

Proposed Problem 82. Area of the Contact Triangle, inradius, circumradius.

3.

Proposed Problem 81. Area of a triangle, side, inradius, circumradius.

2.

Proposed Problem 80. Area of a triangle, side, incircle, inradius.

1.

Proposed Problem 76: Area of a Circle. Square, Circle, Circular Sector.