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Area of a triangle, Theorems and Problems - Table of Content
 

Area of a triangle, Index

 

 
 

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

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

 
 

Routh's theorem index

Routh's Theorem - Index
Triangle, Cevians, Area, Ratio.
 

 

Marion Walter's theorem and related topics

Marion Walter's Theorem and Related Topics: Index
 

Problem 433: Quadrilateral, Area

Proposed Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.
 

Area of a triangle, Cevian, Trisector

Proposed Problem 416.
Triangle, Cevians, Trisectors, Area.
 

Area of a triangle, Circumcircle, Angle Bisector

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

Square, Triangle, Area, Circle

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

Triangle area, Circle, Curvilinear triangle

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

Area of Triangle, Circles, Diameters

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

Square, Exterior point, Triangle, Area

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

Square, Triangle, Area

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

Area of a triangle

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

Problem 273 Triangle and Squares

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

Rectangle, Isosceles Right Triangle, Square, Area

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

 

Elearning: Napoleon Theorem III

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

 

Viviani theorem extension, regular polygon

Proposed Problem 225. Viviani's Theorem Extension, Regular Polygon, Apothem, Distance. Area of triangles. 
 

Viviani theorem, isosceles triangle, extension on the base

Proposed Problem 224. Viviani's theorem, Isosceles triangle, Altitude, Distances, Point on the extension of the base. Area of triangles.  
 

Viviani theorem, Isosceles triangle

Proposed Problem 223. Viviani's theorem, Isosceles triangle, Altitude, Distances. Area of triangles.  
 

Viviani theorem, Equilateral triangle, exterior point

Proposed Problem 222. Viviani's theorem, Equilateral triangle, Exterior point, Distances. Area of triangles.  
 

Viviani's theorem I

Proposed Problem 221. Viviani's theorem, Equilateral triangle, Interior point, Distances. Area of triangles.  
 

Lune of Hippocrates Index

Lune of Hippocrates Index. Area of a right triangle. 
 

Elearn 212: 120 degree triangle, area

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

 

Elearn 211: 60 degree triangle, area

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

 

Elearn 206

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

Right triangle area

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

Elearning 197: Triangle Area

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

 

Elearning 196: Inradius, Exradii

Proposed Problem 196. Area of triangles, Inradius and Exradii Formula.

 

Geometry: Triangle Area, inradius, exradii

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

Area of a triangle, semiperimeter, exradius

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

 

Area of a triangle, semiperimeter, inradius

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

 

Geometry Problem Circle, Diameter, and Chord

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

 

Geometry Problem 191 about triangle and squares

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

 

Circle tangent externally, trapezoid, area

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

Elearning 177: Parallelogram with midpoints, Area

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

Elearning 176: Quadrilateral Area Problem

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

Quadrilateral with Midpoints, Triangles Area

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

Quadrilateral with Midpoints, Triangles Area

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

Elearning 172: Trapezoid, Quadrilateral, Area

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

Elearning 172: Trapezoid, Midpoints, Quadrilaterals, Areas

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

Trapezoid, Triangle, Area

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

Geometry Problem: Parallelogram, Triangles, Pentagon, Area

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

Geometry Problem: Parallelogram, Triangles, Pentagon, Area

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

Geometry Problem: Parallelogram, Triangles, Area

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

Geometry Problem: Parallelogram, Triangles, Area

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

Elearning 165: Parallelogram area

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

Elearning 164: Parallelogram, Triangles, Area

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

Elearning 163 Trapezoid, Triangles, Area

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

Elearning 162 Parallelogram and Triangles Areas

Proposed Problem 162. Parallelogram, Triangles, Areas.  
 

Elearning 161 Parallelogram and Octagon Areas

Proposed Problem 161. Parallelogram, Midpoints, Area of an Octagon, Area of triangles.  
 

Quadrilateral Area, Elearning

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

 

Quadrilateral Area, Midpoint

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

Elearning 142: Triangle area

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

 

Elearning 139: Triangle Area

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

Elearning 125: Area

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

 

Elearning 124: Triangle Area, Similarity

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

 

Elearning 123: Triangle Similarity, Area

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

 

Marion Walter's Theorem

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

 

Elearning 121: Similarity and Area

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

 

Problem 120: Triangle area. Elearning.

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

 

Elearn 119: Triangle area.

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

 

Problem 118

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

 

Elearning 117 Areas

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

 

Geometry Problem 116

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

 

Elearning 115: Problem

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

 

Elearning 114: Area

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

 

Elearning 113: Areas

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

 

Area of Square and triangle, Elearning.

Proposed Problem 112. Area of square and triangle.

 

Contact Triangle Area. Elearning.

Proposed Problem 110. Area of Contact Triangle.

 

Pythagoras curiosity. Online tutoring.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions.

 

Elearning 103.

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

 

Problem 102. Elearning, Online Tutoring

Proposed Problem 102.Equilateral Triangle Area, Interior Point.

 

Elearning 97

Proposed Problem 97. Similar Triangles, Areas.

 

Geometry problem

Proposed Problem 90. Quadrilateral and Triangle Areas, Midpoints.
 

Math problem

Proposed Problem 89. Triangles of equal area, Midpoints.
 

Math problem

Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints.
 

Quadrilateral area problem

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

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.
 

De Gua's Theorem
Area of triangles.
 

Triangle and Squares 22
Area of triangles and rectangles.
 
 

Hippocrates and Squaring the Circle
Triangle areas 
 

Heron's Formula with medians Triangle areas.
 

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.
Triangle areas. 
 

Euclid's Elements 23 definitions

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index
 

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

 

 

 

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