Areas - Table of Content

Area of a Triangle Index.

Varignon and Wittenbauer paralellograms. Quadrilateral: midpoints and trisection points of the edges. Areas.

Proposed Problem 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas.

Proposed Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence.

Proposed Problem 371.
Square, Inscribed circle, Triangle, Area.

Proposed Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area.

Proposed Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters.

Proposed Problem 357.
Square, Exterior point, Triangles, Area.

Proposed Problem 356.
Square, Point inside, Triangles, Area.

Proposed Problem 322.
Square, Inscribed circle, Tangent, Triangle area.

Proposed Problem 280.
Quadrilateral, Perpendiculars, Area of Squares.

Proposed Problem 273.
Triangle, Perpendiculars, Area of Squares.

Proposed Problem 252.
Rectangle, isosceles right triangle, square, area.

Proposed Problem 251.
Parallelogram, sides, diagonals, squares, areas.

Proposed Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.

Proposed Problem 212. 120 Degree Triangle, Equilateral triangles, Areas.

Proposed Problem 211. 60 Degree Triangle, Equilateral triangles, Areas.

Proposed Problem 206. Area of a Right Triangle, Inradius, and Exradius relative to the hypotenuse.

Proposed Problem 205. Right Triangle Area, Exradii relatives to legs or catheti.

Proposed Problem 197. Area of a Triangle, Side, Inradius, and Exradius.

Proposed Problem 196. Triangle, Inradius and Exradii Formula.

Proposed Problem 195. Area of a Triangle, Inradius, Exradii.

Proposed Problem 194. Area of a Triangle, Semiperimeter, Exradius.

Proposed Problem 193. Area of a Triangle, Semiperimeter, Inradius.

Proposed Problem 192. Circle, Diameter, Chord, Perpendicular, Triangle, Area.

Proposed Problem 191. Triangle, Altitudes, Orthocenter, Squares, Areas.

Proposed Problem 180. Circles Tangent Externally, Common External Tangents, Areas.

Proposed Problem 178. Quadrilateral, Trisection of sides, Area.

Proposed Problem 177. Parallelogram with Midpoints, Triangles, Areas.

Proposed Problem 176. Quadrilateral with Midpoints, Triangles, Areas.

Proposed Problem 175. Quadrilateral with Midpoints, Areas.

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

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

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

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

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

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

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

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

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

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

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

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

Proposed Problem 162. Parallelogram, Triangles, Areas.

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

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

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

Proposed Problem 149. Quadrilateral, Area, Midpoints.

Proposed Problem 148. Quadrilateral, Area, Midpoints.

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

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

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

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

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.

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

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

Heron's Formula with medians 

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.
 

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.

Archimedes Proposition 7. Circles and Squares.

Proposition 14 area of the Salinon.

Brahmagupta's Formula  Area of a cyclic quadrilateral.

Brahmagupta Formula Extension Area of any quadrilateral.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions.

Hippocrates and Squaring the Circle
 

Lunes of Hippocrates 4
 

Lunes of Hippocrates 3
 

Lunes of Hippocrates 2
 

Lunes of Hippocrates 1
 

Pythagoras and Circle Area
 

De Gua's Theorem

Triangle and Squares 22
 

Triangle and Squares 21
See also: Triangle and Squares 19

Triangle and Squares 20

Triangle and Squares 19.

Triangle and Squares 18  Sangaku Problem.

Cyclic Quadrilateral: Ratio of the Diagonals
 

Ptolemy's Theorem.
 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Proposed Problem 112. Area of square and triangle.

Proposed Problem 110. Area of Contact Triangle.

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

Proposed Problem 102.Equilateral Triangle Area, Interior Point.

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

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

Proposed Problem 98. Quadrilateral Area, Centroid, Similarity.

Proposed Problem 97. Similar Triangles, Areas.

Proposed Problem 90. Quadrilateral and Triangle Areas, Midpoints.

Proposed Problem 89. Triangles of equal area, Midpoints.

Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints.

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

Proposed Problem 86. Intouch and Extouch Triangles, Areas.

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

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

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

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

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

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

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