Ask Dr. Math

High School Archive

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

Selected answers to common questions:
    Area of an irregular shape.
    Classifying quadrilaterals.
    Heron's formula.
    Polygon diagonals.
    Pythagorean theorem proofs.
    Triangle congruence.

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

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

Isosceles Trapezoid [6/23/1996]

Bases AB and CD of an isosceles trapezoid ABCD are 12 units apart...

Isosceles Trapezoid Proof [01/18/2002]

Given: ABCD is an isosceles trapezoid with bases BC and AD. Prove: ABCD is an isosceles trapzoid.

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.

Isosceles Triangle Maximizes Area? [09/11/2003]

How can you show that among all triangles having a specified base and a specified perimeter, the isosceles triangle on that base has the largest area?

Isosceles Triangle Proof [05/14/2006]

Given triangle ABC, with D on BC and AD bisecting angle A. The center of the circle circumscribing ABC is the same point as the center of the circle inscribed in ADC. Prove that ABC is a isosceles triangle.

Isosceles Triangles [2/8/1996]

A student asks how to find angle B of a given isosceles triangle.

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

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

Kitchen Tabletop [11/21/2001]

I need to determine the correct pivot point...

A Ladder Puzzle [10/20/2000]

A 10-meter ladder is leaning against a wall just touching the corner of a 3-meter cube placed flat against the wall. At what height does the end of the ladder touch the wall?

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?

Lattice Points in a Rectangle [06/04/1999]

How can I prove that in any rectangle centered at (0,0) with an area greater than 4, you can find lattice points other than (0,0)?

Lattice Points on Hypotenuse [10/01/2001]

What is the number of lattice points on the hypotenuse of a right triangle?

The Law of Margins [9/2/1996]

How do I figure out the margins of my mat using the Golden Ratio?

Learning to Read Proofs [10/31/2003]

How do you know what step comes next in a proof?

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 Triangle's Sides [1/23/1995]

I have a triangle problem for you to solve: The lengths of the three sides of a triangle could be...

Length of the Diagonals of a Parallelogram [05/22/2000]

A parallelogram has a 70-degree angle and sides 6cm and 10cm long. How long are its diagonals?

Limited Area, Unlimited Perimeter [11/27/1997]

What is the figure?

Limit of Area [03/01/1998]

Limit approached by area of a square when its sides are repeatedly divided into three congruent parts and squares are constructed outwardly on the middle parts.

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?

Line Dividing a Plane [05/11/2001]

Given a square (graphed on the Cartesian coordinate system) and a point in the square, draw a line through the point that will divide the square into two regions: one the smallest area possible, the other the largest possible.

Lines Intersecting within a Polygon [10/24/1996]

Given an n-sided regular polygon with all vertices connected to each other by straight line segments, how do you determine the number of intersection points within the polygon?

Lines of Symmetry [01/29/2001]

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

Lines of Symmetry in Regular Polygons [03/13/2001]

Is there a formula for finding all the lines of reflectional symmetry in regular polygons?

Locus [05/03/1999]

What is a locus?

Logarithms and the Area of a Triangle [6/3/1996]

Is is true that if A is the area of a triangle, then....log(A) = ...?

Longest Ladder [11/30/2001]

Two hallways, one 8 ft. wide and other 4 ft. wide, meet to form a right angle. What is the longest ladder that can go around the corner where the hallways meet?

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

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

Magic Triangle Puzzle [07/26/2002]

Where did the white square come from?

Making a Pool Tarp [9/27/1995]

I'm trying to construct a pool frame out of pvc that will be placed over a pool. We already have the pool tarp, but we need to build something that will shed water so it has to have a slope. PVC only comes in 90 degree and 45 degree angles and straight sections. How do I figure out the maximum height the frame can stick straight up in the air to utilize the tarp?

Math and Sports [02/26/1997]

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

Maximize Area of Trapezoid [07/28/2003]

Given an isosceles trapezoid with three of its sides of length 10 cm, find the fourth side so that the area is maximized.

Maximum Area of Inscribed Triangle [12/10/2001]

An isosceles triangle is inscribed in a circle of radius R. Find the value of Theta that maximizes the area of the triangle.

Maximum Number of Acute Angles in a 2001-gon [05/29/2002]

What is the largest possible number of acute angles a 2001-gon can have if no two sides cross each other?

Maximum Rectangle within a Quadrilateral [10/25/2001]

I need to extract from a quadrilateral the maximum area rectangle inside it.

Maximum Surface Area [07/03/2003]

Within a rectangle x by y, I wish to draw a shape that is no more than x across in any direction, but which has the largest possible surface area within the confines of the rectangle.

Measures of Interior and Exterior Angles of Polygons [07/07/2005]

A question about star polygons leads to a discussion about calculating interior and exterior angles of polygons.

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