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Dr. Math FAQ:
3D and higher
Browse Middle School Triangles and Other Polygons
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
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
- 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
- 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
- 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
- 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
- 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
- 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
- Dissecting a Square into Acute Triangles [11/09/1999]
Can you dissect a square into a finite number (fewer than 14) of acute
- 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
- 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