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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Rectangle to Parallelogram [06/28/2002]

As you change a rectangle to a parallelogram, what happens to the area and the perimeter?

Reflecting a Triangle [9/14/1996]

A right triangle is reflected about its hypotenuse. What is the new geometric figure that is formed?

Regular and Non-regular Polygon Areas [03/10/1999]

Given a regular and a non-regular polygon with the same perimeter, prove that the area of the regular polygon will always be greater.

Regular Decagon [03/25/2002]

Can you show me a picture of a regular decagon?

Regular vs. Equilateral Polygons [07/24/2003]

What is the difference between a regular polygon and an equilateral polygon?

The Relation of Perimeter to Area [10/2/1995]

I'm puzzled by the ability of two fences with the same perimeter to have very different areas inside them. I realize by LxW an 8' x 10' fence will have more area than a 6' x 12' fence, but WHY? Both fences have 18' surrounding them but different areas. Also does a circle or a square conserve more area with identical perimeters?

Remembering Area Formulas [12/23/2001]

Is there was a good way to help me memorize the formulas for areas of different shapes?

Rhombus and Square Comparison [01/14/2004]

Comparison of the definitions of rhombus and square as a way to answer the questions, 'Is a square a rhombus?' and 'Is a rhombus a square?'.

Rhombus vs. Rhomboid [08/27/2002]

What is the difference between a rhombus and a rhomboid?

Right Angles in a Triangle [3/8/1996]

How many right angles (90 degrees) can a triangle have?

A Right Triangle of Points [01/14/1999]

Determine the values of x that would make the points (x,0), (-2,1), and (3,4) the vertices of a right triangle.

Right Triangles [3/30/1996]

Is there an easy way to remember the different right triangles and how to find the length of missing sides? I already know that in any right triangle: (a*a) + (b*b) = (c*c).

Scale Factor of Similar Shapes [05/12/2000]

Find the scale factor, the ratio of the perimeters, and the ratio of the areas of two regular octagons that have sides of lengths 21 and 28, respectively.

Scalene Triangle [8/20/1996]

Construct a triangle PQR: PQ = 9cm, angle PQR = 38 degrees, and angle QPR = 67 degrees...

Ship's Bearing [8/22/1996]

A ship travels 8km due east and then 8km due north. What is the bearing of the ship from its initial point?

Sides of an Octagon [04/13/1997]

What is the formula for the length of the sides of an octagon whose diameter is 15 feet?

Sides of Similar Triangles [06/11/1998]

The sides of a triangle are 24, 16, and 12. The shortest side of a similar triangle is 6. Find the longest side of this triangle.

Similar Rectangles [05/03/1997]

The outside boundary of an unfolded card is similar to its boundary when it is folded. Find the width of the card if the open length is 8 and the folded length is 4.

Similar Triangles [1/22/1996]

For triangle ABC whose vertices are A(6,3),B(1,5),C(-1,4), what are the vertices of a similar triangle whose perimeter is 5 times that of triangle ABC?

Similar Triangles and Area [11/17/1998]

P is a point on the segment joining midpoints D, E of the sides AB, AC of a triangle ABC. Prove that BPC has twice the area of ADE.

Similar Triangles and Ratios [12/04/2002]

A man who is 54.4 inches tall casts a shadow that is 69.7 inches. His son's shadow is 41 inches. What is the height of the man's son ?

Sine, Co-sine, and Tangent: SOHCAHTOA [03/28/1999]

I am having trouble figuring out what to use when solving a triangle problem.

Six Lines, 4 Triangles [8/19/1996]

How can you form four triangles from six toothpicks?

The Six Quadrilaterals [2/2/1996]

My daughter forgot her textbook and needs to know the 6 types of quadrilaterals.

The Spider and the Fly [12/23/1999]

A spider and a fly are on opposite walls of a rectangular room... Does the spider get the fly?

Square Inscribed in a Circle [09/28/1997]

What percent of the circle is contained within the square?

Square Inside a Square [01/30/2001]

Imagine a square with eight compass points marked at each corner and midpoints of the sides. Create a smaller square inside... How do the areas of the two squares compare, and why?

SSA Theorem: Valid or Invalid? [12/19/2001]

Why can't the SSA Theorem be used to prove congruence?

Stars in a Flag [04/15/1999]

Find the area of the stars in the American Flag.

Straightedge and Compass Constructions [12/14/1998]

Can you help me with these constructions, using only a straightedge and a compass? A 30, 60, 90 triangle, the three medians of a scalene triangle,...

Subsets of Shapes [01/27/2004]

What is the relationship between square and a rectangle?

Summing Odd Numbers Geometrically [10/30/1999]

Can you prove that 1 + 3 + 5 + ... + (2n-1) = n*n by using a simple geometric method?

Sum of Angles inside a Polygon [2/18/1996]

What is the sum of the angles inside a 10-sided polygon?

Sum of Degrees in a Triangle [03/03/1999]

Four proofs that the degrees in a triangle sum to 180.

Sum of the Angles in an N-Pointed Star [11/29/1999]

Can you tell me how to find an equation for the sum of the angles in the tips of an n-pointed star?

Sum of the Angles in a Star [09/21/1999]

How can I find the sum of the measures of the five acute angles that make up a star?

Supplementary Angles in a Parallelogram [10/23/1995]

Are all parallelograms supplementary?

Teaching about Bearings [06/08/2000]

What are bearings? Do you have any ideas on how I can present bearings to my math class in an interesting fashion?

Teaching Area of Triangles [9/15/1996]

When I gave a Unit Assessment, all but one student got area of a triangle wrong. Where did I fail?

Thinking about the Maximum Area Enclosed by a Fence [04/15/2004]

You have 2000 meters of fencing. What is the largest area you can enclose with it using various shapes?

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