Ask Dr. Math

Middle School Archive

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.

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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?

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?

Dividing a Square Cake into Five Equal Pieces [07/28/2001]

How can you divide a square-topped cake that is a rectangular solid and is frosted on all faces into five pieces so that everyone receives the same amount of cake and icing?

Do Figures with Equal Sides Have the Same Area? [11/20/2008]

If a rectangle is tipped slightly so the corners are not square but the side lengths don't change, does the area of the figure change or stay the same?

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