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.
- Ratios and Geometry [10/29/1998]
An airplane flying at 33,000 feet has a visibility of 100 miles. What
percent of the total land area to the horizon is visible?
- 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
- 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
- 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,
- 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
- 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
- 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
- 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
- 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
- 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?