Ask Dr. Math

Middle School Archive

Browse Middle School Triangles and Other Polygons
Stars indicate particularly interesting answers or good places to begin browsing.

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

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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 triangle?

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 inches?

Using a Protractor [06/28/1998]

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

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, and squares.

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 horizontal?

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?

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