Ask Dr. Math

Middle School Archive

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.

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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 points.

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 protractor.

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 different shapes?

Turning a Perimeter into a Scale Factor [02/17/2003]

Perimeter and area ratios of similar figures are given. Find each scale factor.

Using a Protractor [06/28/1998]

How do you construct two parallel lines and intersect them making a 65-degree angle?

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 into algebra?

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...

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?

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