See also the
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.
- 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?
- Thinking about the Maximum Area Enclosed by a Fence [04/15/2004]
You have 2000 meters of fencing. What is the largest area you can
enclose with it using various shapes?
- Three Facts Necessary to Find a Triangle [09/13/2002]
Is there a formula for solving for a right triangle given only the
length of one leg and no angles except for the known 90-degree angle?
- Tiling a Floor [06/30/1999]
How many square yards is a 12ft. by 15ft. room? How many 8" x 8" tiles
would you need for a 30 sq. ft. room?
- Total Area of Multiple Objects [07/18/2002]
I have 6 windows and want to know the total square feet. Do I compute
the areas separately, or add the dimensions and use those to compute
the area all at once?
- Triangle and Trapezium Ratio [10/26/1998]
ABCD is a square with sides of length 4 cm. Find M on BC so that the
ratio of triangle ABM and trapezium ADCM is equal to 1/3.
- Triangle Area [08/13/1997]
How do you find the area of a triangle?
- Triangle Geometry: Sides and Edges [6/2/1996]
If the angles of a triangle are equal, does it necessarily mean that the
sides are also equal?
- Triangle Inequality Theorem [03/09/2001]
The lengths of the sides of a non-isosceles triangle, in size order, are
5, x, and 15. What are all possible integral values of x?
- Triangles: Angle Sums [05/15/2002]
Can you draw a triangle in which the sum of any two angles - no
matter which two you pick - is always less than 120 degrees?
- Triangles: Height and Angle [4/12/1996]
A tree casts a shadow 30 ft and makes an angle of 47 degrees with the
ground. How high is the tree?
- Triangles with Specific Lengths and Angles [3/24/1996]
My base is 32 inches and my angle can not exceed 35 degrees. How long
will my sides be and what is the inside angle?
- A Triangle with Three Right Angles [12/01/1999]
How can you make a triangle with three right angles?
- Two Column Proof of a Theorem [08/12/1998]
Write a two-column proof and give numbered statements with reasons....
- Two-Sided Polygon? [12/01/2003]
My 5th grade math teacher said that we had to draw a polygon using two
straight lines. Is this possible?
- Types of Triangles [02/24/2003]
What is the the difference between equilateral, isosceles, and
scalene triangles? How can I remember which name goes with which
- Understanding Rectangle Area and Perimeter [11/08/2002]
True or false: if the perimeter of a rectangle increases, the
rectangle's area always also increases.
- Units Crossed by a Line Segment [2/2/1996]
If you connect (0,0) to (p,q) where p and q are positive whole numbers,
how many squares do you go through?
- Using a Parallelogram to find the Area of a Triangle [06/26/2001]
What is the area of a triangle with a height of 12 inches and a base of 3
- Using a Protractor [06/28/1998]
How do you construct two parallel lines and intersect them making a
- Venn Diagram to Classify Quadrilaterals [01/02/2003]
I am looking for a Venn diagram that will accurately display the
relation among trapezoids, parallelograms, kites, rhombi, rectangles,
- What Does a Myriagon Look Like? [10/30/2002]
I am looking for a picture of a myriagon.
- What is an N-gon? [06/01/1998]
Can you explain the statement: "In an N-gon, n-3 diagonals can be drawn
from one vertex"?
- What is a Vertex? [12/06/2001]
And what does vertices mean?
- What is Circumference? [06/25/2001]
My friend told me it's somewhat like the measurement of the outside of a
circle, but I don't understand that.
- What is Length in a Rectangle? [05/31/1999]
Is the length of a rectangle the longest side, whether vertical or
- Why are Manhole Covers Round? [05/09/2000]
Why are most manhole covers round? Why aren't manhole covers on the
streets squares or rectangles?
- Why Do the Angles of a Triangle Add to 180 Degrees? [4/17/1996]
We were wondering why all the angles in a triangle add up to 180 degrees.
- Why do the Midpoints of Quadrilaterals Make a Parallelogram? [2/7/1996]
Why is it that if you join the midpoints of any quadrilateral you always
get a parallelogram?
- Why So Many Shapes? [05/07/2001]
I just want to know why there are so many shapes in the world.
- World War II Window Blackout [10/21/2001]
Mr. Brown had a square window 120cm x 120cm, but the only material he
could find was a sheet of plywood 160cm x 90cm; same area, different
shape. He drew some lines and cut out just two congruent shapes, which he
joined to make a square of the correct size. How did he do it?
- You Can't Trisect an Angle [7/16/1996]
Who proved you can't trisect an angle?