Ask Dr. Math Middle School Archive

Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ

 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. Rectangles: Area and Perimeter the Same [4/15/1996] There are two different rectangles whose sides are integers and whose area and perimeter are the same. Find the dimensions. Rectangle to Parallelogram [06/28/2002] As you change a rectangle to a parallelogram, what happens to the area and the perimeter? Reflecting a Triangle [9/14/1996] A right triangle is reflected about its hypotenuse. What is the new geometric figure that is formed? Regular and Non-regular Polygon Areas [03/10/1999] Given a regular and a non-regular polygon with the same perimeter, prove that the area of the regular polygon will always be greater. Regular Decagon [03/25/2002] Can you show me a picture of a regular decagon? Regular vs. Equilateral Polygons [07/24/2003] What is the difference between a regular polygon and an equilateral polygon? The Relation of Perimeter to Area [10/2/1995] I'm puzzled by the ability of two fences with the same perimeter to have very different areas inside them. I realize by LxW an 8' x 10' fence will have more area than a 6' x 12' fence, but WHY? Both fences have 18' surrounding them but different areas. Also does a circle or a square conserve more area with identical perimeters? Remembering Area Formulas [12/23/2001] Is there was a good way to help me memorize the formulas for areas of different shapes? Rhombus and Square Comparison [01/14/2004] Comparison of the definitions of rhombus and square as a way to answer the questions, 'Is a square a rhombus?' and 'Is a rhombus a square?'. Rhombus vs. Rhomboid [08/27/2002] What is the difference between a rhombus and a rhomboid? Right Angles in a Triangle [3/8/1996] How many right angles (90 degrees) can a triangle have? A Right Triangle of Points [01/14/1999] Determine the values of x that would make the points (x,0), (-2,1), and (3,4) the vertices of a right triangle. Right Triangles [3/30/1996] Is there an easy way to remember the different right triangles and how to find the length of missing sides? I already know that in any right triangle: (a*a) + (b*b) = (c*c). Scale Factor of Similar Shapes [05/12/2000] Find the scale factor, the ratio of the perimeters, and the ratio of the areas of two regular octagons that have sides of lengths 21 and 28, respectively. Scalene Triangle [8/20/1996] Construct a triangle PQR: PQ = 9cm, angle PQR = 38 degrees, and angle QPR = 67 degrees... Ship's Bearing [8/22/1996] A ship travels 8km due east and then 8km due north. What is the bearing of the ship from its initial point? Sides of an Octagon [04/13/1997] What is the formula for the length of the sides of an octagon whose diameter is 15 feet? Sides of Similar Triangles [06/11/1998] The sides of a triangle are 24, 16, and 12. The shortest side of a similar triangle is 6. Find the longest side of this triangle. Similar Rectangles [05/03/1997] The outside boundary of an unfolded card is similar to its boundary when it is folded. Find the width of the card if the open length is 8 and the folded length is 4. Similar Triangles [1/22/1996] For triangle ABC whose vertices are A(6,3),B(1,5),C(-1,4), what are the vertices of a similar triangle whose perimeter is 5 times that of triangle ABC? Similar Triangles and Area [11/17/1998] P is a point on the segment joining midpoints D, E of the sides AB, AC of a triangle ABC. Prove that BPC has twice the area of ADE. Similar Triangles and Ratios [12/04/2002] A man who is 54.4 inches tall casts a shadow that is 69.7 inches. His son's shadow is 41 inches. What is the height of the man's son ? Sine, Co-sine, and Tangent: SOHCAHTOA [03/28/1999] I am having trouble figuring out what to use when solving a triangle problem. Six Lines, 4 Triangles [8/19/1996] How can you form four triangles from six toothpicks? The Six Quadrilaterals [2/2/1996] My daughter forgot her textbook and needs to know the 6 types of quadrilaterals. The Spider and the Fly [12/23/1999] A spider and a fly are on opposite walls of a rectangular room... Does the spider get the fly? Square Inscribed in a Circle [09/28/1997] What percent of the circle is contained within the square? Square Inside a Square [01/30/2001] Imagine a square with eight compass points marked at each corner and midpoints of the sides. Create a smaller square inside... How do the areas of the two squares compare, and why? SSA Theorem: Valid or Invalid? [12/19/2001] Why can't the SSA Theorem be used to prove congruence? Stars in a Flag [04/15/1999] Find the area of the stars in the American Flag. Straightedge and Compass Constructions [12/14/1998] Can you help me with these constructions, using only a straightedge and a compass? A 30, 60, 90 triangle, the three medians of a scalene triangle,... Subsets of Shapes [01/27/2004] What is the relationship between square and a rectangle? Summing Odd Numbers Geometrically [10/30/1999] Can you prove that 1 + 3 + 5 + ... + (2n-1) = n*n by using a simple geometric method? Sum of Angles inside a Polygon [2/18/1996] What is the sum of the angles inside a 10-sided polygon? Sum of Degrees in a Triangle [03/03/1999] Four proofs that the degrees in a triangle sum to 180. Sum of the Angles in an N-Pointed Star [11/29/1999] Can you tell me how to find an equation for the sum of the angles in the tips of an n-pointed star? Sum of the Angles in a Star [09/21/1999] How can I find the sum of the measures of the five acute angles that make up a star? Supplementary Angles in a Parallelogram [10/23/1995] Are all parallelograms supplementary? Teaching about Bearings [06/08/2000] What are bearings? Do you have any ideas on how I can present bearings to my math class in an interesting fashion? Teaching Area of Triangles [9/15/1996] When I gave a Unit Assessment, all but one student got area of a triangle wrong. Where did I fail? Page: []

Search the Dr. Math Library:

 Search: entire archive just Middle School Triangles and Other Polygons Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words