|
Area of a triangle, Theorems
and Problems - Table of Content
|
|
 |
|
|
 |
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
Triangle, Cevians, Area, Ratio.
|
|
 |
Marion Walter's Theorem and Related Topics:
Index |
|
 |
Geometry Problem
619
Triangle Area, 30 Degrees, Incircle, Incenter, Tangent. |
|
 |
Geometry Problem
618
Triangle Area, 60 Degrees, Incircle, Incenter, Tangent. |
|
 |
Geometry Problem
617
Right Triangle Area, Incircle, Incenter, Tangent, 90 Degrees. |
|
 |
Problem
579.
Quadrilateral, Diagonals, Triangles, Areas. |
|
 |
Problem
558.
Quadrilateral, Trisection, Sides, Wittenbauer Parallelogram, Area, Auxiliary Lines. |
|
 |
Problem
557.
Quadrilateral, Midpoints, Sides, Varignon Parallelogram, Area, Auxiliary Lines. |
|
 |
Problem
545.
Acute Triangle, Squares, Altitudes, Area, Measure. |
|
 |
Problem
540.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras. |
|
 |
Problem
539.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras. |
|
 |
Proposed Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity. |
|
 |
Proposed Problem 416.
Triangle, Cevians, Trisectors, Area. |
|
 |
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 273.
Triangle, Perpendiculars, Area of Squares. |
|
 |
Proposed Problem 252.
Rectangle, isosceles right triangle, square, area.
|
|
 |
Proposed Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles areas.
|
|
 |
Proposed Problem 225. Viviani's Theorem Extension, Regular Polygon,
Apothem, Distance. Area of triangles. |
|
 |
Proposed Problem 224. Viviani's theorem, Isosceles triangle,
Altitude, Distances, Point on the extension of the base. Area of
triangles. |
|
 |
Proposed Problem 223. Viviani's theorem, Isosceles triangle,
Altitude, Distances. Area of triangles. |
|
 |
Proposed Problem 222. Viviani's theorem, Equilateral triangle,
Exterior point, Distances. Area of triangles. |
|
 |
Proposed Problem 221. Viviani's theorem, Equilateral triangle,
Interior point, Distances. Area of triangles. |
|
 |
Lune of Hippocrates Index.
Area of a right triangle. |
|
 |
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. Area of
triangles, 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, Triangle Areas.
|
|
 |
Proposed Problem 177.
Parallelogram with Midpoints, Triangles, Areas. |
|
 |
Proposed Problem 176.
Quadrilateral with Midpoints, Triangles, 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.
Trapezoid Index |
|
 |
Proposed Problem 162.
Parallelogram, Triangles, Areas.
|
|
 |
Proposed Problem 161.
Parallelogram, Midpoints, Area of an Octagon, Area of triangles.
|
|
 |
Proposed Problem 147.
Quadrilateral, Area, Midpoints, Triangle.
|
|
 |
Proposed Problem 146. Varignon's
Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter.
Triangles. |
|
 |
Proposed Problem 142. Four
Triangles, Incircle, Tangent and Parallel to Side, Areas. |
|
 |
Proposed Problem 139. Triangle
Area, Orthic Triangle, Semiperimeter, Circumradius. |
|
 |
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.
|
|
 |
The Pythagorean Curiosity
Triangles and squares, fifteen conclusions. |
|
 |
Proposed Problem 103.Equilateral
Triangle Area, Interior Point, Heron's Formula.
|
|
 |
Proposed Problem 102.Equilateral
Triangle Area, Interior Point. |
|
 |
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. 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
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.
|
|
 |
|
