Plane Geometry: Areas,Theorems and Problems

Geometry's realm vast,
Areas, theorems, problems cast,
Beauty in shapes last.

Area of a Triangle, Theorems and Problems, Index.

Area of a Right Triangle, Theorems and Problems.

Circle Area. Index.
Theorems and Problems. 
 

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

Marion Walter's Theorem and Related Topics: Index

Geoboard for iPad Pythagorean Theorem Proof by Leonardo.

Geometry Problem 1579: Involving perpendicular diameters, tangents, and triangle areas.

Geometry Problem 1578: Find the Area of a Bicentric Quadrilateral with Perpendicular Extensions of Opposite Sides!.

Geometry Problem 1564: Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints.

Geometry Problem 1546: Discover the Hidden Geometry: Calculate Area of Contact Triangle DEF in Triangle ABC

Geometry Problem 1545: Unlock the Geometric Mystery: Calculate the Area of Triangle ABC with Inscribed Circle and Excenters!

Geometry Problem 1544: Challenge: Calculate the Area of a Triangle with Given Arc and Semicircle Intersections.

Geometry Problem 1543: Calculating the Area of Quadrilateral ABED in a Square with a Side Length of 20 and an Intersecting Arc.

Geometry Problem 1538: Unlocking the Secrets of Triangular Geometry: Solve for the Area of a Quadrilateral Using External Squares and a Segment Length.

Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points?.

Geometry Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals.

Geometry Problem 1494.
Parallelogram, Midpoints, Octagon, Areas.

Geometry Problem 1467.
Square, Rectangle, Triangle, Area.

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 1443.
Triangle Area, Incenter, Circumcenter, 90 Degree, Perpendicular, One-third Area, Art, Poster, Typography, iPad Apps.

Geometry Problem 1439.
Rectangle, Diagonal, Perpendicular, Circles, Areas, Art, Poster, Typography, iPad Apps.

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 1420.
Regular Hexagon, Inscribed Circle, Area, Tangent Circles, Tangent Line.

Geometry Problem 1364.
Square, Inscribed Circle, Area, Angle Bisector, Perpendicular, 45 Degrees, Sketch, iPad Apps.

Geometry Problem 1362.
Equilateral Triangle Inscribed in a Circle, Lunula, Ratio of Areas, Tangent, Sketch, iPad Apps.

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

Problem 1338.
Four Squares, Diagonals, Angle, 45 Degrees, Areas.

Geometry Problem 1333.
Two Squares Side by Side, Three Triangles, Area, Measurement.

Geometry Problem 1332.
Two Squares Side by Side, Triangle, Area.

Geometry Problem 1323.
Square, Angle Trisector, Diagonal, Regular Dodecagon, Area, 30-60 degrees.

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 1204
Square, Triangle, 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 1192
Trapezoid, Triangle, Diagonal, Midpoint, Area, Parallel.

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

Geometry Problem 1187
Triangle, Quadrilateral, Midpoints, Area.

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

Geometry Problem 1185
Similar Rectangles, Four Quadrilaterals, Sum of the Areas, Metric Relations.

Geometry Problem 1182
Two Squares, Four Quadrilaterals, Sum of the Areas, Metric Relations.

Geometry Problem 1171
Area of a Triangle in terms of the three altitude or heights h_a, h_b, h_c.

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

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 1097.
Quadrilateral, Inscribed Circle, 90 Degree, Angle, Area.

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 1078.
Square, Inscribed Circle, Tangent, Triangle, Area.

Geometry Problem 1077.
Chain of Equal Tangent Circles, Circular Sector, Area, Sangaku, Sacred Geometry.

Geometry Problem 1070.
Circle, Chord, Equilateral Triangle, Square, Rectangle, Area, Diameter, Perpendicular.

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

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

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

Geometry Problem 1044.
Triangle, Parallelogram, Midpoint, Area.

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

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

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

Geometry Problem 1030.
Quadrilateral, Triangle, Area, Midpoint, Parallel lines.

Geometry Problem 1016.
Triangle, 45 Degrees, Area, Triangle, Quadrilateral, Altitude, Bisector.

Geometry Problem 1014.
Square, Diagonal, 45 Degrees, Angle, Equal Areas, Triangle, Quadrilateral.

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

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

Geometry Problem 971.
Equilateral Triangle, Rectangle, Common Vertex, Sum of Right Triangles Areas.

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

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

Geometry Problem 961.
Quadrilateral, Trisection, Sides, Sum of Areas.

Geometry Problem 957.
Equilateral Triangle, Inscribed Circle, Incircle, Circumscribed Circle, Circumcircle, Area, Circular Segment.

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