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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 MIDDLE SCHOOL About Math Algebra    equations    factoring expressions    graphing equations Arithmetic    division    exponents    factorials    factoring numbers    fractions/percents    logarithms Definitions Geometry    2-dimensional      conic sections/        circles      triangles/polygons    3D and higher      polyhedra History/Biography Logic Measurement    calendars/      dates/time    temperature    terms/units Number Sense    factoring numbers    negative numbers    pi    prime numbers    square roots Probability Puzzles Ratio/Proportion Statistics Word Problems Browse Middle School Triangles and Other Polygons Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Classifying quadrilaterals.     Polygon diagonals.     Pythagorean theorem proofs. Base or Width? [06/11/2002] When computing area, is there a difference between 'width' and 'base'? Can a Circle be a Polygon? [5/22/1996] Could a circle be considered a polygon with an infinite number of sides? Can a Rhombus Be a Square? [01/15/2004] General strategy to determine if one geometric shape definition also applies to another geometric figure. Centroid, Circumcenter, Incenter, Orthocenter: Etymologies [01/20/2002] Why are the points centroid, circumcenter, orthocenter, and incenter named as they are, and are there any other special points associated with triangles? Characteristics of an Orthocenter [11/12/1999] What are some characteristics of the orthocenter of a triangle? Circles and Squares [4/3/1996] Given a large circle with a square inside it (the sides of the square are equal to the radius of the larger circle and are chords of the circle) and a smaller circle inside the square... Classifying Triangles [06/04/2002] Given the lengths of the sides of a triangle, determine whether the triangle is acute, right, or obtuse. Cleaning the Ice [09/09/1997] The hockey rink is a rectangle, 120 ft. by 60 ft. The scraper cleans a 4- ft.-wide strip... on which trip will it have cleaned half the area of the rink? Concave and Convex Polygons [08/13/2001] What's the difference between a convex and a concave polygon? Congruent Triangles - SSS Test [11/16/1998] How do you know if two triangles are congruent? Constructing a Segment [09/26/1999] Given a 1" segment and a 2.5" segment, how can you find a segment of length sqrt(2.5)" using only a compass and a straightedge? Constructing the Orthocenter [01/27/1999] How do you construct the orthocenter of a triangle? Constructing Triangles [3/6/1996] How do you construct 30-60-90 triangles with a compass and a straight edge? Converting Areas: Square Feet to Square Inches [03/18/1997] How many square inches are in ten square feet? Convex and Concave Polygons [3/23/1996] What are convex and concave polygons? Convex Polygons [2/5/1996] Students from Sweet Home Middle school ask many questions about convex polygons. Convex Polygons and Other Questions [1/22/1996] A 7th grade geometry class asks some questions about area and perimeter. Counting Rectangles Cut By a Diagonal [06/15/1999] How can we find an equation for the number of unit squares that are cut by a line going from corner to corner on a rectangle? Counting Sides by Counting Diagonals [06/04/2002] How can I find the number of sides in a polygon, given the number of diagonals? Covering Paper using Index Cards [10/24/2001] What is the maximum area of an 8"x13" sheet of paper that you can cover by using seven 3"x5" standard index cards? Cutting a Circle out of a Square [2/14/1996] What is the area (to the nearest square centimeter) of the largest circle that can be cut from a square piece of sheet metal 73cm. on each side? Explain how you determined this. Decagons [05/04/1997] What does a decagon look like? Deducing Dimensions without Algebra, with Area and Perimeter: Which Clue First? [10/21/2017] Given its perimeter and area, a teen struggles to use the former to determine a rectangle's dimensions without algebra. Doctor Ian breaks it down a different way; emphasizing strategic problem-solving throughout, he shares a more effective example. Defining the Term Oblong [05/15/2000] Can you give a definition of the term "oblong"? Definition of Opposite Sides [01/18/2001] What is the formal definition of 'opposite sides' of a polygon? Does a regular pentagon have opposite sides? Does a concave polygon have opposite sides? How can we define it consistent with our intuition? De Longchamp's Point [09/21/2000] What is De Longchamp's point, and how is it used? Determining Triangle Similarity [05/26/1998] Given two triangles, how can you determine if they are similar? Diagonals and Axes of Symmetry [03/31/1998] Could you explain the concepts behind the diagonals and axes of symmetry in a regular octagon? Diagonals and Tiles [11/17/2001] Jay tiled a 15x21' rectangular ballroom with 1 ft. sq. tiles. Then he drew diagonals connecting opposite corners of the room. How many tiles did the diagonals pass through? Diameter of the Base of a Cone [08/12/1998] How do you find the formula to calculate the diameter of the base of a cone of nine degrees at various lengths? Dimensions of a Rectangle [8/26/1996] Find the original dimensions of a rectangle whose area is increased by 81 square meters. Dissecting a Square into Acute Triangles [11/09/1999] Can you dissect a square into a finite number (fewer than 14) of acute triangles? Distance Between Opposite Corners of a Box [05/09/2002] A moth is sitting in the lower left front corner of a storage shed. What is the length of the shortest path that the moth can fly to the upper right back corner of the shed? Distance Between Points of Tangency [03/20/1999] What is the distance between the contact points of two smaller circles in contact with a larger circle...? Distance between Two Points [08/03/1999] I'm trying to find an equation to measure the distance between 2 points on a 3D plane. Distance to an Object [04/07/2000] Is there an easy way to measure the distance from a baseline to an object if one knows the measurement of the baseline and both angles leading toward the object? Dividing a 30-60-90 Triangle in Four [08/07/1999] Find four different ways to divide a 30-60-90 triangle into four triangles similar to and each having 1/4 the area of the original triangle. Dividing A Cake - A Math Puzzle [12/20/1998] How can you cut a 9" square two-layer cake into 13 pieces so that each piece has exactly the same amount of cake and frosting? Dividing a Hexagon into 8 Equal Parts [06/11/1999] How can you divide a regular hexagon into 8 equal parts? Dividing a Square [07/31/1999] A large square is divided into several equal-sized smaller squares using x lines. How can I find a formula for the number of smaller squares produced? Page: []

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