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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How Tall is Hal? [04/18/2001]

Hal is standing 40 feet away from a 36-ft. tree. If the distance from the top of the tree to the top of Hal's head is 50 ft., how tall is Hal?

How to Increase the Sides to Double the Area of a Square [01/28/2005]

I am puzzled as to how you would double the area of a square. Do you multiply the sides by some decimal?

How Wide is the Garden? [01/06/1998]

A rectangular garden has a 136-ft. fence around it. The garden is 40 feet long. How wide is it?

Importance of Surface Area [05/26/2001]

Why is surface area so important? What kinds of things depend on surface area?

Inclusive and Exclusive Definitions [04/05/2001]

Are squares rectangles? Are rectangles squares?

Inclusive vs. Exclusive Definitions [01/24/2002]

My geometry teacher says that a square is not also a rhombus, a rectangle, and a parallelogram. Please help!

Inscribing a Regular Pentagon within a Circle [04/15/1999]

What are the reasons for the steps in inscribing a regular pentagon within a circle with only the help of a compass and a straightedge?

Insufficient Altitude [10/09/2003]

The base of a triangle is 1200 ft. The altitude is 500 ft. What is the length of the third side?

Inverse Pythagorean Theorem [05/10/2001]

How can you tell a triangle is a right triangle without looking at the triangle and just how long the sides are?

Is a Circle a Polygon? [03/07/1999]

A circle is not a polygon.

Is an Equilateral Triangle Also Isosceles? [02/19/2008]

Can equilateral triangles also be classified as isosceles? In other words, does an isosceles triangle have exactly two equal sides or at least two equal sides?

Is a Square a Rectangle? [06/04/1997]

Are squares rectangles? What is a pentagon?

Is a Star Concave or Convex? [4/2/1996]

Is a star-shaped polygon convex?

Is Kite the True Name? [03/29/2002]

Is kite the true math name for this shape, or is there another?

Isosceles Triangle - Angles [11/06/1996]

Given that one base angle of an isosceles triangle is 39 degrees, find the measure of the other two angles in the triangle.

Is This a Square? [01/30/2001]

Given four points on a graph, what can I do to verify this is a square?

Kites And Triangles [11/02/1998]

What are kites, and how are they related to triangles?

Largest Triangle in a Square [10/31/1998]

If the area of a square is 1, what is the largest area of a triangle constructed inside the square? How would you prove it?

Least Perimeter [10/13/2002]

Finding a formula for least perimeter of a square or rectangle.

Left-Sided Rhombuses in a Larger Rhombus [05/22/2000]

How many left-sided, right-sided, and vertical rhombuses can be found in a larger NxN rhombus?

Leg of a Triangle [04/02/2002]

I need to know where the name "leg" of a triangle comes from, or what its origin is.

Length of a Rectangle Side [8/24/1996]

The length of a rectangle is 9 cm more than half the width...

The Length of the Sides of Polygons [3/7/1996]

How many feet should each side be in a regular octagon / hexagon / pentagon if the area is 7,000 square feet?

Length, Width of Rectangle Given Perimeter [9/4/1996]

If the perimeter of a rectangle is 300 and the length is two times the width...

Letter Names for Triangles [05/16/2000]

When a triangle is named by the letters of its vertices, why are the letters in the order they are? Could they be in any order?

Linear Systems of Equations in Two Variables [06/18/1999]

How can I find the length of AE, EB and DC, given that parallelogram ABCD has a perimeter of 50, trapezoid AECD has a perimeter of 39, and AE = EC?

Lines of Symmetry [01/29/2001]

How do you find the number of lines of symmetry there are in a polygon?

Lines of Symmetry [03/17/1997]

What are lines of symmetry?

Ludolph van Ceulen and Pi [11/02/1998]

How did Ludolph van Ceulen estimate pi by inscribing and circumscribing a circle with squares?

Making a Parallelogram [06/19/2001]

Make five shapes - a parallelogram, a square, and three triangles - into one parallelogram.

Making Triangles [11/12/2001]

Make a triangle that contains 180 degrees without using a protractor.

Math and Sports [02/26/1997]

Can you give me information on how math relates to sports?

Measuring the Height of a Building Using Shadows [05/24/2000]

What time of day is best to use a shadow to measure the height of a building by using triangles?

Medians of a Triangle [02/16/1999]

Prove that the 3 medians of a triangle divide themselves up into a ratio of 1:2.

Mid-segment Theorem [02/02/1999]

Can you help me prove the Mid-Segment Theorem?

Minimum Distance [5/22/1995]

Inside a rectangular room a spider is at a point on the middle of one of the end walls and a fly is on the opposite wall. What is the shortest distance the spider must crawl to reach the fly?

Names of Polygons [9/13/1995]

What is the correct name for an eleven-sided polygon?

Names of Triangles and Angles [07/25/2001]

My teacher told me to find names of triangles other than equilateral and isosceles.

Name That Polygon [12/03/1999]

Can you help me figure out what kind of polygons are being described based on these clues?

Naming Corresponding Parts of Congruent Figures [04/23/2003]

Given triangle OPS congruent to triangle TQR, name the corresponding sides and angles of the two triangles.

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