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Word Problems

Browse Middle School Two-Dimensional Geometry
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Classifying quadrilaterals.
    Pythagorean theorem proofs.

Circumference vs. Perimeter [05/09/2003]
Technically speaking, can the term 'perimeter' apply to a circle in a mathematical context?

Classification of Angles by Size [09/30/2008]
What do you call an angle that is greater than 180 degrees?

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?

Complementary and Supplementary Angles [09/30/1998]
Why are angles called complementary and supplementary?

Complementary and Supplementary Angles [10/24/1999]
Definitions of complementary and supplementary angles.

Complementary or Supplementary? [04/02/2001]
I keep getting complementary and supplementary mixed up. How can I remember which is which?

Connection Between Circumference and Surface Area [05/08/1998]
Can you explain the connection between the circumference of a circle and the surface area of a sphere?

Constructing a One-Degree Angle [05/25/2000]
Is it possible to contruct a one degree angle using only a straightedge and compass?

Converting Areas: Square Feet to Square Inches [03/18/1997]
How many square inches are in ten square feet?

Converting Square Feet to Square Yards [09/13/1997]
I need to know how to change sq. ft. to sq. yds. for carpeting.

Converting Square Inches to Square Feet [02/26/1998]
How many square inches are in ten square feet?

Converting Square Yards to Square Feet [9/12/1996]
57.33 sq. yds. equals ____ sq. ft?

Converting to Square Units [01/07/2002]
How do I convert 47,224 sq. miles to kilometers?

Convex Polygons and Other Questions [1/22/1996]
A 7th grade geometry class asks some questions about area and perimeter.

Coordinates in the Cartesian Plane [01/21/2005]
How do I get the coordinates for a point on a graph?

Counting Angles and Rays [8/23/1995]
What is the algebraic expression to show the relation of the number of angles created as rays are added from a common point?

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?

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 Slits in a Piece of Paper [02/01/2002]
How can you cut a hole in a piece of paper so a person can go through it?

Defining a Square Centimeter [04/09/2002]
Why is the area of a unit square the product of the two sides?

Defining Distance Mathematically [10/16/1996]
What is wrong with D' = sqrt(X^2 - X'2)?

A Definition of Clinometer [12/10/1995]
We've been surfing the net to find a definition of 'clinometer' and have been unsuccessful.

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?

Definition of Oval [06/09/2002]
Can you give a precise definition of 'oval'?

Degrees and Radians, Explained [03/19/2002]
How do you find the degree measure for an angle from pi/60 rad?

Degrees in Complementary and Supplementary Angles [10/28/2002]
What are complements and supplements?

Deriving Pi [05/10/2001]
I know that Pi is equivalent to 3.14, but what formulas are used to come up with 3.14?

Deriving the Area Formula for a Circle [03/08/2000]
Why is the area of a circle the square of the radius times pi?

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 Endpoint [01/26/2003]
The center of a circle is (-4,7) and one endpoint of a diameter is (2,-1). What is the other endpoint of the diameter?

Dimensions [08/30/2001]
What are 1-dimensional, 2-dimensional, and 3-dimensional? What's the difference?

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.

Dividing Land by Area vs. Perimeter [11/05/1999]
What are the advantages of dividing land by area vs. perimeter?

Do Parallel Lines Intersect? [3/1/1996]
I have heard that parallel lines can in fact intersect. Is this true?

Eleven Nets of a Cube [11/15/2001]
My teacher says that there are 11 combinations to make a cube without reversing them, but I can only find 6.

Eleven Sections of Fence [05/29/2003]
I have a grid containing 16 squares. Each square represents 1 acre. I need to draw 11 sections of fence along the dotted lines of the squares so that 4 fields are formed, each containing 4 acres of land.

Equable Shapes [04/26/2001]
Is there a rule for how to get equable shapes, that is, shapes with the same area and perimeter?

Estimating Seating Capacity [05/10/2000]
How can I estimate how many chairs can be placed in the seating area of a convention center meeting room that is 80 feet across at the front, 120 feet across at the rear, and 150 feet from front to back?

Etymologies of Algebra, Geometry, Trigonometry [10/22/2001]
What are the origins and roots of the words geometry, algebra, and trigonometry?

Euclid's Parallel Postulate [2/14/1995]
We are studying Euclid's Parallel Postulate. Why did mathematicians disagree with him? What other geometries resulted from this disagreement? What postulate replaced the Parallel Postulate?

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