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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.
- How Many Proofs of the Pythagorean Theorem? [03/27/2003]
Do you know the exact number of proofs of the Pythagorean Theorem in
- How Many Triangles Have Sides Whose Lengths Total 15? [5/6/1995]
How many triangles can one construct with integral sides adding up to 15?
- How Tall is Hal? [04/18/2001]
Hal is standing 40 feet away from a 36-ft. tree. If the distance from the
top of the tree to the top of Hal's head is 50 ft., how tall is Hal?
- How to Increase the Sides to Double the Area of a Square [01/28/2005]
I am puzzled as to how you would double the area of a square. Do you
multiply the sides by some decimal?
- How Wide is the Garden? [01/06/1998]
A rectangular garden has a 136-ft. fence around it. The garden is 40 feet
long. How wide is it?
- Importance of Surface Area [05/26/2001]
Why is surface area so important? What kinds of things depend on surface
- Inclusive and Exclusive Definitions [04/05/2001]
Are squares rectangles? Are rectangles squares?
- Inclusive vs. Exclusive Definitions [01/24/2002]
My geometry teacher says that a square is not also a rhombus, a
rectangle, and a parallelogram. Please help!
- Inscribing a Regular Pentagon within a Circle [04/15/1999]
What are the reasons for the steps in inscribing a regular pentagon
within a circle with only the help of a compass and a straightedge?
- Insufficient Altitude [10/09/2003]
The base of a triangle is 1200 ft. The altitude is 500 ft. What is the
length of the third side?
- Inverse Pythagorean Theorem [05/10/2001]
How can you tell a triangle is a right triangle without looking at the
triangle and just how long the sides are?
- Is a Circle a Polygon? [03/07/1999]
A circle is not a polygon.
- Is an Equilateral Triangle Also Isosceles? [02/19/2008]
Can equilateral triangles also be classified as isosceles? In other
words, does an isosceles triangle have exactly two equal sides or at
least two equal sides?
- Is a Square a Rectangle? [06/04/1997]
Are squares rectangles? What is a pentagon?
- Is a Star Concave or Convex? [4/2/1996]
Is a star-shaped polygon convex?
- Is Kite the True Name? [03/29/2002]
Is kite the true math name for this shape, or is there another?
- Isosceles Triangle - Angles [11/06/1996]
Given that one base angle of an isosceles triangle is 39 degrees, find
the measure of the other two angles in the triangle.
- Is This a Square? [01/30/2001]
Given four points on a graph, what can I do to verify this is a square?
- Kites And Triangles [11/02/1998]
What are kites, and how are they related to triangles?
- Largest Triangle in a Square [10/31/1998]
If the area of a square is 1, what is the largest area of a triangle
constructed inside the square? How would you prove it?
- Least Perimeter [10/13/2002]
Finding a formula for least perimeter of a square or rectangle.
- Left-Sided Rhombuses in a Larger Rhombus [05/22/2000]
How many left-sided, right-sided, and vertical rhombuses can be found in
a larger NxN rhombus?
- Leg of a Triangle [04/02/2002]
I need to know where the name "leg" of a triangle comes from, or what its
- Length of a Rectangle Side [8/24/1996]
The length of a rectangle is 9 cm more than half the width...
- The Length of the Sides of Polygons [3/7/1996]
How many feet should each side be in a regular octagon / hexagon /
pentagon if the area is 7,000 square feet?
- Length, Width of Rectangle Given Perimeter [9/4/1996]
If the perimeter of a rectangle is 300 and the length is two times the
- Letter Names for Triangles [05/16/2000]
When a triangle is named by the letters of its vertices, why are the
letters in the order they are? Could they be in any order?
- Linear Systems of Equations in Two Variables [06/18/1999]
How can I find the length of AE, EB and DC, given that parallelogram ABCD
has a perimeter of 50, trapezoid AECD has a perimeter of 39, and AE = EC?
- Lines of Symmetry [01/29/2001]
How do you find the number of lines of symmetry there are in a polygon?
- Lines of Symmetry [03/17/1997]
What are lines of symmetry?
- Ludolph van Ceulen and Pi [11/02/1998]
How did Ludolph van Ceulen estimate pi by inscribing and circumscribing a
circle with squares?
- Making a Parallelogram [06/19/2001]
Make five shapes - a parallelogram, a square, and three triangles - into
- Making Triangles [11/12/2001]
Make a triangle that contains 180 degrees without using a protractor.
- Math and Sports [02/26/1997]
Can you give me information on how math relates to sports?
- Measuring the Height of a Building Using Shadows [05/24/2000]
What time of day is best to use a shadow to measure the height of a
building by using triangles?
- Medians of a Triangle [02/16/1999]
Prove that the 3 medians of a triangle divide themselves up into a ratio
- Mid-segment Theorem [02/02/1999]
Can you help me prove the Mid-Segment Theorem?
- Minimum Distance [5/22/1995]
Inside a rectangular room a spider is at a point on the middle of one of
the end walls and a fly is on the opposite wall. What is the shortest
distance the spider must crawl to reach the fly?
- Names of Polygons [9/13/1995]
What is the correct name for an eleven-sided polygon?
- Names of Triangles and Angles [07/25/2001]
My teacher told me to find names of triangles other than equilateral and