Geometry: Area of a triangle, Theorems and Problems - Table of Content
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![Area of a Triangle, Theorems and Problems](../math_geometry_online_courses/area_of_a_triangle_1.jpg) |
Geometry's realm,
Triangle's area unfolds,
Theorems guide us,
Challenging problems arise,
Wisdom gained, beauty revealed. |
![](../heron/heron__proof_170x100.jpg) |
Heron's Formula.
Key facts and
a purely geometric
step-by-step proof. |
![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. |
![](../Varignon_Wittenbauer_170.jpg) |
Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and
trisection points of the edges. Triangle areas.
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![Routh's theorem index](routh's_theorem_index_17.jpg) |
Routh's Theorem - Index
Triangle, Cevians, Area, Ratio.
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![Marion Walter's theorem and related topics](marion_walter_theorem_index.jpg) |
Marion Walter's Theorem and Related Topics:
Index |
![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 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 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. |
![Geometry Problem 1458](../school-college/5/p1458-incircle-excircle-triangle-area-1.jpg) |
Geometry
Problem 1458.
Triangle, Incircles, Excircle, Area, Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1456](../school-college/5/p1456-orthocenter-triangle-similarity-circles-geogebra-ipad-1.jpg) |
Geometry
Problem 1456.
Altitudes, Orthic Triangle, Circumcircle, Parallel lines, Similarity, Area,
iPad. Step-by-step illustration using GeoGebra. |
![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 1391](../school-college/4/p1391-triangle-ratio-area-circumcircle-1.jpg) |
Geometry Problem 1391. Two Triangles, Ratio of Areas, Circumcircle. |
![Problem 1381 Parallelogram, Triangle, Area](../school-college/4/p1381-parallelogram-triangle-area-1.jpg) |
Geometry Problem 1381. Parallelogram, Exterior Point, Triangle, Area. |
![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 1310](../school-college/4/p1310-square-triangle-area-measurement-1.jpg) |
Geometry Problem 1310.
Square, Center, Right Triangle, Area, Measurement. |
![Geometry problem 1305](../school-college/4/p1305-triangle-angle-bisector-circumcircle-perpendicular-area-1.jpg) |
Geometry Problem 1305.
Triangle, Circumcircle, Angle Bisector, Arc, Perpendicular, Area. |
![Heron Triangle Area Medians](../heron/heron_medians_170x100.jpg) |
Geometry Problem 1296. Heron's Formula, Area of a
triangle in terms of the three
medians. |
![Geometry problem 1288](../school-college/3/p1288-triangle-50-100-degrees-measurement-1.jpg) |
Geometry Problem 1288.
Triangle, 30-50-100 Degrees, Area, Inradius, Metric Relations, Measurement. |
![Geometry problem 1287](../school-college/3/p1287-isosceles-triangle-40-100-40-degrees-1.jpg) |
Geometry Problem 1287.
Triangle, 40-100-40 Degrees, Congruence, Area, Metric Relations, Measurement. |
![Geometry problem 1279](../school-college/3/p1279-parallelogram-area-midpoint-triangle-1.jpg) |
Geometry Problem 1279.
Parallelogram, Midpoint, Triangle, Area, 3/10. |
![Geometry problem 1274](../school-college/3/p1274-isosceles-triangle-80-20-80-measurement-1.jpg) |
Geometry Problem 1274.
Isosceles Triangle, 80-20-80 Degrees, Area, Inradius, Circumradius, Angle Bisector, Metric Relations, Measurement. |
![Geometry problem 1252](../school-college/3/p1252-hexagon-triangle-area-orthocenter-circumcircle-mind-map-1.jpg) |
Geometry Problem 1252.
Triangle, Circle, Circumcircle, Altitude, Area, Hexagon, Perpendicular, 90 Degrees. Mind Map. |
![Geometry problem 1249](../school-college/3/p1249-cyclic-quadrilateral-bisector-triangle-area-1.jpg) |
Geometry Problem 1249.
Cyclic Quadrilateral, Circle, Triangle, Circumcircle, Angle Bisector, Parallel Lines, Area. |
![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 1201](../school-college/3/p1201-triangle-interior-perpendicular-bisector-side-area-1.jpg) |
Geometry Problem 1201
Triangle, Interior Perpendicular Bisector, Midpoint, 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 1197](../school-college/2/p1197-four-squares-triangles-area-1.jpg) |
Geometry Problem 1197
Four Squares, Four Triangles, 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 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 1160](../school-college/2/p1160-triangle-square-areas-equivalent-1.jpg) |
Geometry Problem 1160.
Triangle, Three Squares, Area, Equivalent Triangles. |
![Geometry problem 1155](../school-college/2/p1155-right-triangle-altitude-incenters-area-1.jpg) |
Geometry Problem 1155.
Right Triangle, Altitude, Incenter, Incircle, Area. |
![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 1111](../school-college/2/p1111-right-triangle-square-angle-bisector-area-geometric-mean-math-1.jpg) |
Geometry Problem
1111.
Right Triangle, External Squares, Cathetus, Angle Bisector, Area, Geometric Mean. |
![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 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 1057](../school-college/1/p1057-circle-tangent-secant-diameter-perpendicular-area-math-1.jpg) |
Geometry Problem
1057.
Triangle, Area, Circle with Perpendicular Diameters, Tangent, Secant. |
![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 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 1036](../school-college/1/p1036-triangle-3-equal-circles-incircle-inradius-1.jpg) |
Geometry Problem
1036.
Triangle, Three equal Incircles, Tangent lines, Inradius, Equal Inradii. |
![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 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 981](../school-college/p981-triangle-cevian-concurrent-midpoint-hexagon-area-1.jpg) |
Geometry Problem 981.
Triangle, Concurrent Cevians, Midpoints, Area, Hexagon. |
![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. |
![Problem 928](../school-college/p928-triangle-area-median-cevian-concurrency-1.jpg) |
Geometry Problem 928.
Triangle, Midpoint, Median, Cevian, Concurrency, Area.
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![Geometry Problem 880](../school-college/p880-triangle-midpoint-perpendicular-hexagon-area-parallelogram-1.jpg) |
Geometry Problem 880
Triangle, Midpoints, Sides, Perpendiculars, Hexagon, Area. |
![Geometry Problem 876](../school-college/p876-equilateral-triangle-perpendicular-equal-area-1.jpg) |
Geometry Problem 876
Equilateral Triangle, any Point, Perpendicular, Right Triangle Area, Sum of Areas. |
![Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence](../school-college/p860-triangle-three-medians-area-1.jpg) |
Geometry Problem 860
Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence. |
![Problem 854: Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent lines](../school-college/p854-triangle-parallelogram-parallel-area-similarity-1.jpg) |
Geometry Problem 854
Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent lines. |
![Regular Hexagon, Midpoints, Equilateral Triangle](../school-college/p791-regular-hexagon-midpoint-equilateral-triangle-area-1.jpg) |
Geometry Problem 791
Regular Hexagon, Midpoints of Side and Diagonal, Equilateral Triangle, Area. |
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Post a comment | by Antonio Gutierrez
Last updated:
Jun 29, 2023
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