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 TOPICS This page:   triangles/polygons    Search   Dr. Math See also the Dr. Math FAQ:   geometric formulas and   naming polygons   and polyhedra and   Pythagorean theorem Internet Library:   triangles/polygons HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Triangles and Other Polygons Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Area of an irregular shape.     Classifying quadrilaterals.     Heron's formula.     Polygon diagonals.     Pythagorean theorem proofs.     Triangle congruence. Perimeter Equals Area in a Triangle [4/2/1996] When will the area and perimeter of a right triangle be numerically equal? Perimeter of an Inscribed Regular Polygon [12/10/1998] What is the formula for the perimeter of a regular polygon inscribed inside a circle? Perimeter of a Right Triangle [08/14/2001] What is the perimeter of a right triangle with hypotenuse 65 that can be circumscribed about a circle with radius 12? Perimeter of a Strange Figure [03/23/2002] I don't understand how to find the area or perimeter of a shape that looks like a rectangle with a small triangle to the left on top... Perimeter of Octagon [04/02/1997] What is the perimeter of a an octagonal garden with a diameter of six feet? Pi and Polygons [03/14/1999] Derive a formula to find the angle of an n-sided polygon with x sides. Pick's and Euler's Theorems [05/06/1999] What is Pick's theorem and how can it be linked with Euler's theorem? Pick's Formula [05/22/1997] What is Pick's Formula? Pick's Theorem [9/4/1996] Could you explain Pick's Theorem? Picture Frame, Triangle Measurements [5/20/1996] My teacher gave us ten questions to answer and I could do all except two: 1) A framed rectangular picture is 35cm long and 25cm wide... 2) The base of a triangle is 9cm more than the perpendicular height... Picture of Icosahedron [7/31/1996] Do you have a picture of an icosahedron? Pipe Needed for Natural Gas Line [09/03/1997] Two houses are 130 metres apart at distances of 55 and 105 metres... Pixels in a Triangle [08/02/1999] How can I find the number of pixels inside a triangle? Placing Coins That Touch [8/7/1996] How many 20-cent coins can you put around a 20-cent coin so that all of them touch? A Point Inside a Square [09/18/2003] Point P lies inside square ABCD such that P's distance from A is 1, P's distance from B is 4 and P's distance from C is 5. What is the area of the square? Point Inside or Outside Triangle? [08/02/2001] I have coordinates of three vertices of the triangle and coordinates of the point. A Point in the Triangle [02/12/1999] Finding the point P in a plane of triangle ABC, where PA + PB +PC is minimum. Point within a Triangle [05/29/2003] I have the coordinates of the three corners of a equilateral triangle ABC. How can I decide whether an arbitrary point (X,Y) lies in the plane of the triangle? Pole in a Box [02/09/1999] Can a pole 6.5m long fit into a truck with dimensions of 3m, 3.5m, and 4m? Polygon Algorithms [05/10/2001] Given a polygon as a set of points (X, Y) and a database table with X and Y columns, select all records/points from the table that are inside the polygon or belong to its border. Polygon Diagrams [05/11/2003] I would like to see pictures of polygons with 11, 12, 13, 14, and 15 sides. Polygon Names II [12/11/2003] Why is the triangle named "triANGL"', unlike all the other polygons, which have names like "quadriLATERAL" or "pentaGON"? Polygons and Triangles [03/09/1999] Prove that after splitting a regular n-polygon into n triangles, the isosceles triangles have greater area than the scalene triangles. Polygons, Infinite Sides, and Circles [04/03/1997] Can a regular polygon with an infinite number of sides be a circle? Polyominoes [09/08/1997] I am using polyominos, but I do not know how to tell my dad what they are. How can I tell him so he will know? A Practical Use for the Orthocenter [03/07/2001] Does the orthocenter of a triangle have any practical uses? Probability in the Infinite Plane [03/29/2003] Three randomly drawn lines intersect so as to form a triangle on an infinite plane. What is the probability that a randomly selected point will fall inside that triangle? Probability of Making Triangle with Three Stick Pieces [02/24/2007] Take a stick of unit length and break it into two pieces, choosing the break point at random. Now break the longer of the two pieces at a random point. What is the probability that the three pieces can be used to form a triangle? Proof by Contradiction [09/25/1997] Prove that no isoceles right triangle exists which has all three sides integers. Proof: Median of a Trapezoid Theorem [03/24/2001] Prove that the median of a trapezoid is: 1) parallel to its bases; 2) length = 1/2 the sum of the bases. Proof of Congruency [10/13/1996] Line PR bisects angles QPS and QRS; prove that segments RQ and RS are congruent. Proof of Hero's formula [09/08/1997] Could you tell me where to find a proof of Hero's formula or help on how to derive it? Proof of Morley's Theorem [08/09/2000] How can I prove Morley's theorem (if every angle in a triangle is trisected, each pair of trisectors meets in a point, and all three points form the vertices of an equilateral triangle)? Proof of Pappus' Theorem [04/02/2001] How can I prove Pappus' theorem of colinearity with the help of Menelaus' theory? Proof of Pythagorean Theorem: Pythagoras' Reasoning [02/23/1998] I would like to know how Pythagoras reasoned his theorem. Proof of the Feuerbach Theorem [03/14/2000] Please submit the proof of the Feuerbach theorem (the nine-point circle is tangent to the incircle and the circumcircle of a triangle.) Proof of the Parallelogram Law [08/07/1999] How do you prove the parallelogram law geometrically, without using vectors? Proofs with Isosceles Triangles [10/28/1998] What are altitudes, angle bisectors, and medians? How do you prove that in an isoseles triangle, the altitude is a median and an angle bisector? Proof Using Coordinate Geometry [06/08/2001] In equilateral triangle ABC, a segment is drawn from point A to the side BC at a point (D)... prove that angle BFC (or EFC) is a right angle. Properties Defined, and Undefined [06/21/2016] A teen wonders if all the properties of scalene and isosceles triangles apply to equilateral ones. With the Euler line as a counterexample, Doctor Floor shows that sidelength does matter. Page: []

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