# Geometry: Area of a triangle, Theorems and Problems - Table of Content

Geometry's realm,
Triangle's area unfolds,
Theorems guide us,
Challenging problems arise,
Wisdom gained, beauty revealed.

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

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

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

Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1463.
Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1458.
Triangle, Incircles, Excircle, Area, Step-by-step Illustration using GeoGebra.

Geometry Problem 1456.
Altitudes, Orthic Triangle, Circumcircle, Parallel lines, Similarity, Area, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1430.
Regular Octagon, Area, Equivalent Figures, Poster, Conformal Mapping.

Geometry Problem 1428.
Intersecting Circles, Tangent Line, Triangle, Square, Area.

Geometry Problem 1426.
Two Squares, Collinear Points, Triangle, Quadrilateral, Sum of the Areas.

Geometry Problem 1424.
Triangle, Parallelogram, Trapezoid, Area, Diagonal, Measurement.

Geometry Problem 1423.
Triangle, Area, Three Equal Angles, Circumradius, Measurement.

Geometry Problem 1422.
Triangle, Transversal, Cevian, Area, Measurement.

Geometry Problem 1391.
Two Triangles, Ratio of Areas, Circumcircle.

Geometry Problem 1381.
Parallelogram, Exterior Point, Triangle, Area.

Geometry Problem 1345.
Three Equilateral Triangles, Center, Area, Common Vertex.

Geometry Problem 1310.
Square, Center, Right Triangle, Area, Measurement.

Geometry Problem 1305.
Triangle, Circumcircle, Angle Bisector, Arc, Perpendicular, Area.

Geometry Problem 1296.
Heron's Formula, Area of a triangle in terms of the three medians.

Geometry Problem 1288.
Triangle, 30-50-100 Degrees, Area, Inradius, Metric Relations, Measurement.

Geometry Problem 1287.
Triangle, 40-100-40 Degrees, Congruence, Area, Metric Relations, Measurement.

Geometry Problem 1279.
Parallelogram, Midpoint, Triangle, Area, 3/10.

Geometry Problem 1274.
Isosceles Triangle, 80-20-80 Degrees, Area, Inradius, Circumradius, Angle Bisector, Metric Relations, Measurement.

Geometry Problem 1252.
Triangle, Circle, Circumcircle, Altitude, Area, Hexagon, Perpendicular, 90 Degrees. Mind Map.

Geometry Problem 1249.
Cyclic Quadrilateral, Circle, Triangle, Circumcircle, Angle Bisector, Parallel Lines, Area.

Geometry Problem 1211
Right Triangle, Altitude, Angle Bisector, 45 Degrees, Metric Relations, Area.

Geometry Problem 1208
Triangle, Circle, Excircle, Excenter, Diameter, Perpendicular, 90 Degrees, Equal Areas.

Geometry Problem 1201
Triangle, Interior Perpendicular Bisector, Midpoint, Area.

Geometry Problem 1200
Square, Right Triangle, Perpendicular, 90 Degrees, Equal Areas.

Geometry Problem 1198
Right Triangle, Square, Rectangle, Quadrilateral, Altitude, Equal Areas.

Geometry Problem 1197
Four Squares, Four Triangles, Equal Areas.

Geometry Problem 1192
Trapezoid, Triangle, Diagonal, Midpoint, Area, Parallel.

Geometry Problem 1188
Triangle, Parallelogram, Parallel Lines, Trapezoid, Area.

Geometry Problem 1187

Geometry Problem 1186
Right Triangle, Square, Inscribed Circle, Tangent, Quadrilateral, Area.

Geometry Problem 1171
Area of a Triangle in terms of the three altitude or heights ha, hb, hc.

Geometry Problem 1170
Area of a Triangle in terms of the three sides, a-b-c.

Geometry Problem 1160.
Triangle, Three Squares, Area, Equivalent Triangles.

Geometry Problem 1155.
Right Triangle, Altitude, Incenter, Incircle, Area.

Geometry Problem 1131.
Triangle Area, Two Cevians, Equal Product of Areas.

Geometry Problem 1124.
Triangle, Median, Two Squares, Area.

Geometry Problem 1123.
Hexagon, Triangle, 90 Degrees, Perpendicular Lines, Vertices, Area.

Geometry Problem 1112.
Triangle, Excenters, Circumcircle, Circle, Hexagon, Area.

Geometry Problem 1111.
Right Triangle, External Squares, Cathetus, Angle Bisector, Area, Geometric Mean.

Geometry Problem 1091.
Square, Perpendicular, Distance, Area, Center.

Geometry Problem 1089.
Square, Semicircle, Tangent, Triangle, Area.

Geometry Problem 1082.
Square, Circle, Center, Radius, Side, Isosceles Triangle, 90 Degrees, Area.

Geometry Problem 1058.
Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle, Circle, Diameter.

Geometry Problem 1057.
Triangle, Area, Circle with Perpendicular Diameters, Tangent, Secant.

Geometry Problem 1055.
Triangle, Altitude, Perpendicular, Area, Circumradius, Circle.

Geometry Problem 1051.
Triangle, Square, Semicircle, Arc, Area.

Geometry Problem 1037.
Triangle, Three equal Incircles, Tangent lines, Inradius, Length.

Geometry Problem 1036.

Geometry Problem 1035.
Triangle, Three equal Incircles, Tangent lines, Equivalent triangles, Equal area.

Geometry Problem 1033.
Triangle, Angle Obtuse, Circumcircle, Diameter, Area.

Geometry Problem 983.
Regular Hexagon, A point and six triangles, Areas.

Geometry Problem 982.
Triangle, Excenters, Excentral Triangle, Circumcenter, Area, Hexagon.

Geometry Problem 981.
Triangle, Concurrent Cevians, Midpoints, Area, Hexagon.

Geometry Problem 969.
Equilateral Triangle, Rectangle, Common Vertex, Right Triangles Areas.

Geometry Problem 962.
Triangle, Two Cevians, Areas, Equal Products.

Geometry Problem 928.
Triangle, Midpoint, Median, Cevian, Concurrency, Area.

Geometry Problem 880
Triangle, Midpoints, Sides, Perpendiculars, Hexagon, Area.

Geometry Problem 876
Equilateral Triangle, any Point, Perpendicular, Right Triangle Area, Sum of Areas.

Geometry Problem 860
Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence.

Geometry Problem 854
Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent lines.

Geometry Problem 791
Regular Hexagon, Midpoints of Side and Diagonal, Equilateral Triangle, Area.

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