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Dr. Math FAQ:
3D and higher
Browse Middle School Two-Dimensional Geometry
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Pythagorean theorem proofs.
- Area and Perimeter [05/01/2001]
I do not understand area and perimeter - can you explain them?
- Area and Volume [04/10/2002]
I cannot figure out how to do volume.
- Explementary Angles [05/29/2003]
What do we call two angles that add up to 360 degrees?
- Find Equation for Two Points [12/12/2002]
I want to know how to find an equation for two given coordinate
- Finding Areas using Unit Conversions [3/19/1996]
How do you calculate area, expressed in English units? For example: how
do you calculate the area of a rectangle, where one side is, say, 2
miles, 3 furlongs, 4 yards, 2 feet and 5 inches...?
- How to Measure Angles [04/19/1998]
How do you measure angles? What are degrees and radians?
- Measuring Angles with a Protractor [02/28/2002]
I want to know how to measure acute, reflex and obtuse angles with a
- Painting Cubes [01/06/2003]
How many unit cubes would be needed to create a cube with a side
length of 3 units? If you painted the larger cube and broke it up
into unit cubes, how many faces of each unit cube would be painted?
- Remembering Area Formulas [12/23/2001]
Is there was a good way to help me memorize the formulas for areas of
- Turning a Perimeter into a Scale Factor [02/17/2003]
Perimeter and area ratios of similar figures are given. Find each
- Using a Protractor [06/28/1998]
How do you construct two parallel lines and intersect them making a
- A 14-Sided Polygon [7/28/1996]
What is the proper name for a 14-sided figure?
- 2 Square Feet vs. 2 Feet Square [11/22/1998]
What is the difference between 2 square feet and 2 feet square?
- About Basic Geometry [10/14/1998]
Who developed basic geometry? What is it used for? Who uses it?
- Abraham Kaestner and Euclid's Fifth (Parallel) Postulate [12/02/1996]
Where can I find information on Abraham Kaestner?
- Adjacent Angles [09/19/2001]
What is the definition of adjacent angles?
- The Algebra of Complements and Supplements [01/25/1999]
What are complements and supplements? How do you translate these concepts
- Alternate and Corresponding Angles [10/21/1996]
Please explain corresponding and alternate angles.
- Alternate Exterior Angles [06/03/2002]
What is an 'alternate exterior angle'?
- Angles: Acute, Right, Obtuse, Reflex [06/06/2001]
How can I remember what the names of angles mean?
- Angles as Turns [05/29/2003]
How can angles be negative?
- Angles Greater than 360 Degrees [01/01/1999]
We know the definitions of acute, obtuse, and reflex angles, but we were
debating what kind of angle a 425 degree angle is.
- Angle, Side Length of a Triangle [9/4/1996]
What is the relation between the angles and side lengths of a triangle?
- Angles in a Diagram [10/14/1998]
In a diagram with perpendicular, parallel, and transversal lines, how can
you find the measure of the angles given the measure of one angle?
- Angles of Stars [08/18/1997]
What are the interior and external angles of stars built on regular
pentagons and octagons.
- Area and Perimeter [10/4/1995]
I have a problem with finding area and perimeter - can you help me?
- Area and Perimeter: Mowing the Lawn [6/1/1996]
How many circuits are necessary to cut half the lawn?
- Area Larger Than Perimeter? [04/15/2002]
Can the area of a shape be larger than the perimeter?
- Are Angles Dimensionless? [08/31/2003]
If you look at the dimensions in the equation arc length = r*theta, it
appears that angles must be dimensionless. But this can't be right.
Or can it?
- Area of a Circle with Radius less than 1 [02/18/2002]
If the radius is less than 1 it just gets smaller and you get a smaller
- Area of an Irregular Polygon [03/29/2001]
How can I find the area of an irregular polygon? What about a polygon
made out of rectangles?
- Area of an L [07/10/2003]
How do you find the area of an 'L' shaped object?
- Area of a Rectangle Outside a Rectangle [6/11/1996]
Find the area of the concrete border of a rectangular swimming pool.
- Areas of Figures Broken into Rectangles [10/17/2001]
Calculate the area of each figure. First divide the figure into
rectangles and squares...
- Area, Surface Area, and Volume: How to Tell One Formula from Another [01/18/1999]
Unit dimensions -- and even an idea from calculus -- can tell you which
formula you're using.
- Area: Triangle vs. Rectangle [4/30/1996]
Why do you have to use a different formula to get the area of a triangle
than a rectangle or square?
- Area vs. Perimeter of Rectangles [03/19/2000]
Can you explain how two rectangles with exactly the same perimeter can
enclose different areas?
- Arrange 7 Points in a Plane... [10/05/1998]
Arrange 7 points in a plane so that if any three are chosen, at least 2
of them will be a unit distance apart.
- Building Two Column Proofs [09/12/1998]
We just started learning proofs, and I don't understand how to figure out
the ordering. Can you explain?
- Circle Area and Square Units [11/12/1997]
Is pi metres squared the same as 10,000 pi centimetres squared? Does a
square with sides of 10m have an area of 10m squared or 100 square metres
- or are these the same?