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![College Geometry Online, eLearning](../machu_picchu_h1_810.jpg)
Plane Geometry: Areas,Theorems and Problems
Geometry's realm vast,
Areas, theorems, problems cast,
Beauty in shapes last.
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![Areas](areas_measurement_17.jpg) |
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![Area of a Triangle, Theorems and Problems](../math_geometry_online_courses/area_of_a_triangle_1.jpg) |
Area
of a Triangle, Theorems and Problems, Index.
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![Area of a Right Triangle, Theorems and Problems](../geometry/area-of-right-triangle-theorems-problems-i.jpg) |
Area of a Right Triangle, Theorems and Problems. |
![Area of a Circle](../circle/area-of-a-circle-theorems-problems-index.jpg)
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Circle Area.
Index.
Theorems and Problems.
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![](../Varignon_Wittenbauer_170.jpg) |
Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and
trisection points of the edges. Areas.
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![Marion Walter's theorem and related topics](marion_walter_theorem_index.jpg) |
Marion Walter's Theorem and Related Topics:
Index |
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Geoboard
for iPad Pythagorean Theorem Proof by Leonardo. |
![Geometry Problem 1546](../school-college/6/p1546-inscribed-circle-given-sides-calculate-contact-triangle-area-1.jpg) |
Geometry Problem 1546: Discover the Hidden Geometry: Calculate Area of Contact Triangle DEF in Triangle ABC |
![Geometry Problem 1545](../school-college/6/p1545-geometric-puzzle-area-of-triangle-inscribed-circle-excenters-incircle-1.jpg) |
Geometry Problem 1545: Unlock the Geometric Mystery: Calculate the Area of Triangle ABC with Inscribed Circle and Excenters! |
![Geometry Problem 1544](../school-college/6/p1544-calculate-area-triangle-with-given-arc-semicircle-intersection-geometry-resource-1.jpg) |
Geometry Problem 1544: Challenge: Calculate the Area of a Triangle with Given Arc and Semicircle Intersections. |
![Geometry Problem 1543](../school-college/6/p1543-square-circle-arc-mindpoint-quadrilateral-area-school-college-1.jpg) |
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](../school-college/6/p1538-triangle-external-squares-quadrilateral-area-segment-length-math-class-1.jpg) |
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](../school-college/6/p1537-parallelogram-midpoint-triangle-area-intersection-math-challenge-1.jpg) |
Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points?. |
![Geometry Problem 1536](../school-college/6/p1536-quadrilateral-midpoint-area-triangle-math-education-1.jpg) |
Geometry
Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals. |
![Geometry Problem 1494](../school-college/5/p1494-parallelogram-midpoints-octagon-area-1.jpg) |
Geometry
Problem 1494.
Parallelogram, Midpoints, Octagon, Areas. |
![Geometry Problem 1467](../school-college/5/p1467-square-rectangle-equal-area-geogebra-ipad-1.jpg) |
Geometry Problem 1467.
Square, Rectangle, Triangle, Area. |
![Geometry Problem 1465](../school-college/5/p1465-tangential-quadrilateral-incenter-equal-sum-area-1.jpg) |
Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1464](../school-college/5/p1464-quadrilateral-midpoint-equal-sum-area-1.jpg) |
Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1463](../school-college/5/p1463-parallelogram-equal-sum-area-triangles-geogebra-1.jpg) |
Geometry Problem 1463.
Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
![Problem 1443](../school-college/5/p1443-triangle-area-incenter-90-degree-circumcenter-1.jpg) |
Geometry Problem 1443.
Triangle Area, Incenter, Circumcenter, 90 Degree, Perpendicular, One-third
Area, Art, Poster, Typography, iPad Apps. |
![Problem 1439](../school-college/5/p1439-rectangle-diagonal-perpendicular-circle-ipad-apps-1.jpg) |
Geometry Problem 1439.
Rectangle, Diagonal, Perpendicular, Circles, Areas, Art, Poster, Typography, iPad Apps. |
![Problem 1430](../school-college/5/p1430-regular-octagon-area-1.jpg) |
Geometry Problem 1430. Regular Octagon, Area, Equivalent Figures,
Poster, Conformal Mapping. |
![Problem 1428](../school-college/5/p1428-circle-tangent-triangle-square-area-1.jpg) |
Geometry Problem 1428. Intersecting Circles, Tangent Line, Triangle, Square, Area. |
![Problem 1426](../school-college/5/p1426-two-squares-triangle-quadrilateral-area-1.jpg) |
Geometry Problem 1426. Two Squares, Collinear Points, Triangle, Quadrilateral, Sum of the Areas. |
![Problem 1424](../school-college/5/p1424-parallelogram-triangle-trapezoid-area-1.jpg) |
Geometry Problem 1424. Triangle, Parallelogram, Trapezoid, Area, Diagonal, Measurement. |
![Problem 1423](../school-college/5/p1423-triangle-equal-angle-similarity-area-1.jpg) |
Geometry Problem 1423. Triangle, Area, Three Equal Angles, Circumradius, Measurement. |
![Problem 1422](../school-college/5/p1422-triangle-cevian-transversal-area-1.jpg) |
Geometry Problem 1422. Triangle, Transversal, Cevian, Area, Measurement. |
![Problem 1420](../school-college/5/p1420-circle-area-regular-hexagon-tangent-1.jpg) |
Geometry Problem 1420. Regular Hexagon, Inscribed Circle, Area, Tangent
Circles, Tangent Line. |
![Geometry problem 1364](../school-college/4/p1364-square-inscribed-circle-chord-pieces-area-1.jpg) |
Geometry Problem 1364.
Square, Inscribed Circle, Area, Angle Bisector, Perpendicular, 45 Degrees, Sketch, iPad Apps. |
![Geometry problem 1362](../school-college/4/p1362-equilateral-triangle-inscribed-circle-lunula-area-1.jpg) |
Geometry Problem 1362.
Equilateral Triangle Inscribed in a Circle, Lunula, Ratio of Areas, Tangent, Sketch, iPad Apps. |
![Geometry problem 1345](../school-college/4/p1345-equilateral-triangle-common-vertex-center-area-1.jpg) |
Geometry Problem 1345. Three Equilateral Triangles, Center, Area, Common Vertex. |
![Geometry problem 1338](../school-college/4/p1338-square-45-degrees-diagonal-area-tutoring-1.jpg) |
Problem 1338.
Four Squares, Diagonals, Angle, 45 Degrees, Areas.
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![Geometry problem 1333](../school-college/4/p1333-two-squares-three-triangles-area-1.jpg) |
Geometry Problem 1333.
Two Squares Side by Side, Three Triangles, Area, Measurement. |
![Geometry problem 1332](../school-college/4/p1332-two-squares-side-by-side-triangle-area-1.jpg) |
Geometry Problem 1332.
Two Squares Side by Side, Triangle, Area. |
![Geometry problem 1323](../school-college/4/p1323-square-equilateral-triangle-dodecagon-1.jpg) |
Geometry Problem 1323.
Square, Angle Trisector, Diagonal, Regular Dodecagon, Area, 30-60 degrees. |
![Geometry problem 1211](../school-college/3/p1211-right-triangle-altitude-bisector-45-degrees-class-1.jpg) |
Geometry Problem 1211
Right Triangle, Altitude, Angle Bisector, 45 Degrees, Metric
Relations, Area. |
![Geometry problem 1208](../school-college/3/p1208-triangle-excenter-diameter-perpendicular-area-1.jpg) |
Geometry Problem 1208
Triangle, Circle, Excircle, Excenter, Diameter, Perpendicular, 90 Degrees, Equal Areas. |
![Geometry problem 1204](../school-college/3/p1204-square-triangle-area-class-1.jpg) |
Geometry Problem 1204
Square, Triangle, Area. |
![Geometry problem 1200](../school-college/2/p1200-square-triangles-90-degrees-area-1.jpg) |
Geometry Problem 1200
Square, Right Triangle, Perpendicular, 90 Degrees, Equal Areas. |
![Geometry problem 1198](../school-college/2/p1198-right-triangle-square-rectangle-quadrilateral-area-1.jpg) |
Geometry Problem 1198
Right Triangle, Square, Rectangle, Quadrilateral, Altitude, Equal Areas. |
![Geometry problem 1192](../school-college/2/p1192-trapezoid-triangle-midpoint-area-1.jpg) |
Geometry Problem 1192
Trapezoid, Triangle, Diagonal, Midpoint, Area, Parallel. |
![Geometry problem 1188](../school-college/2/p1188-triangle-parallelogram-area-trapezoid-congruence-parallel-1.jpg) |
Geometry Problem 1188
Triangle, Parallelogram, Parallel Lines, Trapezoid, Area. |
![Geometry problem 1187](../school-college/2/p1187-triangle-quadrilateral-hexagon-midpoint-area-1.jpg) |
Geometry Problem 1187
Triangle, Quadrilateral, Midpoints, Area. |
![Geometry problem 1186](../school-college/2/p1186-right-triangle-square-circle-tangent-area-1.jpg) |
Geometry Problem 1186
Right Triangle, Square, Inscribed Circle, Tangent, Quadrilateral, Area. |
![Geometry problem 1185](../school-college/2/p1185-two-similar-rectangles-sum-areas-metric-relations-1.jpg) |
Geometry Problem 1185
Similar Rectangles, Four Quadrilaterals, Sum of the Areas, Metric Relations. |
![Geometry problem 1182](../school-college/2/p1182-two-squares-sum-areas-metric-relations-1.jpg) |
Geometry Problem 1182
Two Squares, Four Quadrilaterals, Sum of the Areas, Metric Relations. |
![Geometry problem 1171](../school-college/2/p1171-area-a-triangle-altitude-height-ha-hb-hc-terms-proof-1.jpg) |
Geometry Problem 1171
Area of a Triangle in terms of the three altitude or
heights ha, hb, hc. |
![Geometry problem 1170](../school-college/2/p1170-area-of-a-triangle-three-sides-a-b-c-proof-1.jpg) |
Geometry Problem 1170
Area of a Triangle in terms of the three sides, a-b-c. |
![Geometry problem 1131](../school-college/2/p1131-triangle-area-cevian-equal-product-problem-solving-1.jpg) |
Geometry Problem 1131.
Triangle Area, Two Cevians, Equal Product of Areas. |
![Geometry problem 1124](../school-college/2/p1124-triangle-median-square-area-math-1.jpg) |
Geometry Problem 1124.
Triangle, Median, Two Squares, Area. |
![Geometry problem 1123](../school-college/2/p1123-triangle-perpendicular-hexagon-area-math-1.jpg) |
Geometry Problem 1123.
Hexagon, Triangle, 90 Degrees, Perpendicular Lines, Vertices, Area. |
![Geometry Problem 1112](../school-college/2/p1112-triangle-excenter-circumcircle-hexagon-area-math-1.jpg) |
Geometry Problem
1112.
Triangle, Excenters, Circumcircle, Circle, Hexagon, Area. |
![Geometry Problem 1097](../school-college/1/p1097-quadrilateral-area-inscribed-circle-radius-90-degree-1.jpg) |
Geometry Problem
1097.
Quadrilateral, Inscribed Circle, 90 Degree, Angle, Area. |
![Geometry Problem 1091](../school-college/1/p1091-square-center-perpendicular-area-metric-relations-tutor-math-1.jpg) |
Geometry Problem
1091.
Square, Perpendicular, Distance, Area, Center. |
![Geometry Problem 1089](../school-college/1/p1089-square-semicircle-tangent-triangle-area-tutoring-math-1.jpg) |
Geometry Problem
1089.
Square, Semicircle, Tangent, Triangle, Area. |
![Geometry Problem 1082](../school-college/1/p1082-square-circle-isosceles-triangle-area-90-degrees-class-math-1.jpg) |
Geometry Problem
1082.
Square, Circle, Center, Radius, Side, Isosceles Triangle, 90 Degrees, Area. |
![Geometry Problem 1078](../school-college/1/p1078-square-circle-triangle-area-class-math-1.jpg) |
Geometry Problem
1078.
Square, Inscribed Circle, Tangent, Triangle, Area. |
![Geometry Problem 1077](../school-college/1/p1077-equal-tangent-circles-area-sector-sangaku-sacred-geometry-math-1.jpg) |
Geometry Problem
1077.
Chain of Equal Tangent Circles, Circular Sector, Area, Sangaku, Sacred Geometry. |
![Geometry Problem 1070](../school-college/1/p1070-circle-square-rectangle-area-problem-solving-tutorial-1.jpg) |
Geometry Problem
1070.
Circle, Chord, Equilateral Triangle, Square, Rectangle, Area, Diameter, Perpendicular. |
![Geometry Problem 1058](../school-college/1/p1058-triangle-sum-area-altitude-circle-diameter-perpendicular-math-1.jpg) |
Geometry Problem
1058.
Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle, Circle, Diameter. |
![Geometry Problem 1055](../school-college/1/p1055-triangle-area-altitude-circumradius-perpendicular-math-1.jpg) |
Geometry Problem
1055.
Triangle, Altitude, Perpendicular, Area, Circumradius, Circle. |
![Geometry Problem 1051](../school-college/1/p1051-square-triangle-circle-semicircle-arc-area-math-1.jpg) |
Geometry Problem
1051.
Triangle, Square, Semicircle, Arc, Area. |
![Geometry Problem 1044](../school-college/1/p1044-quadrilateral-parallelogram-area-math-1.jpg) |
Geometry Problem
1044.
Triangle, Parallelogram, Midpoint, Area. |
![Geometry Problem 1037](../school-college/1/p1037-triangle-3-equal-circles-incircle-inradius-length-1.jpg) |
Geometry Problem
1037.
Triangle, Three equal Incircles, Tangent lines, Inradius, Length. |
![Geometry Problem 1035](../school-college/1/p1035-triangle-3-equal-circles-incircle-equivalent-area-1.jpg) |
Geometry Problem
1035.
Triangle, Three equal Incircles, Tangent lines, Equivalent triangles, Equal area. |
![Geometry Problem 1033](../school-college/1/p1033-triangle-obtuse-circumcircle-diameter-area-math-1.jpg) |
Geometry Problem
1033.
Triangle, Angle Obtuse, Circumcircle, Diameter, Area. |
![Geometry Problem 1030](../school-college/1/p1030-quadrilateral-triangle-area-midpoint-parallel-online-math-1.jpg) |
Geometry Problem
1030.
Quadrilateral, Triangle, Area, Midpoint, Parallel lines. |
![Geometry Problem 1016](../school-college/1/p1016-triangle-45-degrees-angle-altitude-bisector-quadrilateral-area-math-1.jpg) |
Geometry Problem
1016.
Triangle, 45 Degrees, Area, Triangle, Quadrilateral, Altitude, Bisector. |
![Geometry Problem 1014](../school-college/1/p1014-square-45-degree-angle-diagonal-area-math-1.jpg) |
Geometry Problem
1014.
Square, Diagonal, 45 Degrees, Angle, Equal Areas, Triangle, Quadrilateral. |
![Geometry Problem 983](../school-college/p983-regular-hexagon-point-triangle-area-1.jpg) |
Geometry Problem 983.
Regular Hexagon, A point and six triangles, Areas. |
![Geometry Problem 982](../school-college/p982-triangle-excenter-circumcenter-hexagon-area-1.jpg) |
Geometry Problem 982.
Triangle, Excenters, Excentral Triangle, Circumcenter, Area, Hexagon. |
![Geometry Problem 971](../school-college/p971-equilateral-triangle-rectangle-common-vertex-sum-areas-1.jpg) |
Geometry Problem 971.
Equilateral Triangle, Rectangle, Common Vertex, Sum of Right Triangles Areas. |
![Geometry Problem 969](../school-college/p969-equilateral-triangle-rectangle-common-vertex-sum-areas-1.jpg) |
Geometry Problem 969.
Equilateral Triangle, Rectangle, Common Vertex, Right Triangles Areas. |
![Geometry Problem 962](../school-college/p962-triangle-area-cevian-equal-products-1.jpg) |
Geometry Problem 962.
Triangle, Two Cevians, Areas, Equal Products. |
![Geometry Problem 961](../school-college/p961-quadrilateral-trisect-side-sum-areas-1.jpg) |
Geometry Problem 961.
Quadrilateral, Trisection, Sides, Sum of Areas. |
![Geometry Problem 957](../school-college/p957-equilateral-triangle-incircle-circuncircle-circular-segment-area-1.jpg) |
Geometry Problem 957.
Equilateral Triangle, Inscribed Circle, Incircle, Circumscribed Circle, Circumcircle, Area, Circular Segment. |
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| by Antonio Gutierrez
Last updated:
Jun 29, 2023
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