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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Find the Length of a Carpet [5/3/1996]

A carpet is placed diagonally in a rectangular room...

Find the Length of the Hypotenuse [05/08/2003]

The medians to the legs of a right triangle are 10 and 12.649 or 4 radical 10.

Find the Length of the Third Side [08/26/2003]

Two cars start at the same point, going in opposite directions for six miles; both make a left turn and go 8 more miles. How many miles apart are the cars?

Find the Orthocenter [11/04/1998]

Given three points (-2,4) (7,2) (3,8), find the orthocenter.

Find the Perimeter [04/09/2002]

I have a group of 13 rectangles arranged into a larger rectangle. I know the area, but I need to find the perimeter.

Finite vs. Rational [9/10/1996]

A right triangle with sides 1 and 2 has a hypotenuse equal to the square root of 5, which is irrational - it carries on to infinity without recurring - but the side length of a triangle must be finite!

Fitting a Picture to a Frame [11/14/1996]

I have a picture frame that needs to have twice as much border on the side of the picture as on the top. If the photo is half the area of the frame, how wide should the borders be?

Five Equal Pieces of a Square Cake [05/22/2001]

Ravina wants to cut a square cake using straight vertical cuts to make five pieces of equal volume. If she makes the first cut from the cake's center to the top left corner, where must she make the other cuts if they all start from the cake's center?

Formula for Area of Any Regular Polygon [03/01/1998]

Area of a regular polygon, given the number of sides and length of a side.

Formula for the Area of a Trapezoid [01/14/2006]

My math teacher gave us the formula for the area of a trapezoid, but I don't understand his explanation of why it works. Can you explain it?

Formula for the Trapezoid Rule [07/31/1999]

I am writing a program to find the moment area of any shape...

Formulas: Width, Side Length of Octagon [03/24/1997]

Given the width of an octagon, what is the length of a side, and vice-versa?

The Geodesic Dome [8/4/1995]

What polygons make up a geodesic dome and where are they located?

Geodesics [12/15/1996]

Can you give me information on the math behind geodesics?

Geometrically Completing the Square [08/07/1997]

What are the steps for geometrically completing the square?

Geometric Interpretation of Inequality [8/23/1996]

If z1 and z2 are complex numbers, interpret geometrically the inequality | z1 + z2 | < | z1 | + | z2 |.

Geometric Proof of Area of Triangle Formula [04/30/2008]

I'm trying to prove the formula that the area of a triangle with coordinates (0,0), (x1,y1), and (x2,y2) is 1/2(x1y2 - x2y1) without using determinants. Seems like I saw one years ago, but I can't recall it.

Geometric Proof of Heron's Formula [01/25/2000]

How can I prove Hero(n)'s formula using a circle with center P and radius R inscribed in triangle ABC?

Geometric Proof of the Steiner-Lehmus Theorem [05/13/2002]

If two bisectors of two angles of a triangle are equal then the triangle is an isosceles triangle. Is there a geometric proof of this?

Geometry Ladder Problem [12/9/1995]

A figure shows a 12-foot ladder leaning across a 5-foot fence and touching a higher wall located 3ft behind the fence. You want to find the distance x from the base of the ladder to the bottom of the fence. . .

Geometry of a Pizza [5/31/1996]

How can you divide a slice in half by cutting across a wedge?

Geometry Proof Involving Circle and Triangle [09/26/2005]

Triangle ABC cuts a circle at points E, E', D, D', F amd F'. Prove that if AD, BF and CE are concurrent, than AD', BF' and CE' are also concurrent.

Geometry Unit on Quilting [07/16/1997]

Do you have any information/units/lessons/curriculum ideas on quilting in mathematics?

Given a Triangle with Angles a,b,c [05/03/1999]

Show that cos(a)+cos(b)+cos(c) is less than or equal to 3/2.

Given Octagon Diameter, Find Side Length [04/09/2003]

If you have the diameter of an octagon, what formula gives you the length of the sides?

Golden Ratio and the Sine of 18 [04/17/2001]

2*sin(18) + 1 is equal to the golden ratio. Is there any significance to this?

Golden Triangle: An Isosceles Triangle [01/23/2001]

What is the Golden Triangle?

Golden Triangle: What is It? [09/19/1999]

What is a Golden Triangle?

Grazing Half of a Square Field [08/30/2001]

My cow is tied to the middle of one side of a SQUARE field. What is the length the rope should be to enable the cow to eat half the grass?

Handshakes and Polygon Diagonals [09/12/2001]

If a polygon has 42 sides, how many diagonals does it have?

Height of a Dome [08/06/2002]

On a perfectly circular, small, flat island, a glass dome covers the island, forming a perfect hemisphere. If the canopy is 10 feet tall at the center of the island, how far from the center can 6-foot-tall Omar walk upright?

Height of a Trapezoid [02/08/2002]

A trapezoid has parallel bases of lengths 5 and 30, and non-parallel sides of length 5 and 25. Find the height of the trapezoid.

Height of Intersection [01/16/2003]

Two flagpoles of heights 10 and 70 feet are 100 ft. apart on a level surface. If a line runs from the top of each pole to the bottom of the other, what is the height of the intersection?

Height of Parallelogram or Trapezoid [04/30/1999]

Could you explain the concept of height with regard to a parallelogram or a trapezoid?

Heron's Formula [04/11/2003]

How can I find the area of an isosceles triangle, an equilateral triangle, a scalene triangle, an obtuse-angle triangle and an acute-angle triangle without the height being given?

Heron's Formula, Cartesian Coordinate Plane [11/01/2001]

If a triangle has sides 5, 6, and the square root of thirteen, what is the area of the triangle?

A Hexagon Inscribed within a Circle [2/29/1996]

A hexagon is inscribed within a circle. Three consecutive sides have a length of 3 and the other three consecutive sides have a length of 5. A chord is drawn within the circle....

Hexagon Sides, Length of a Beam [2/1/1995]

I am totally stumped on these two word problems. They are driving me crazy!

Hexagon vs. Hexagram [01/11/1999]

What is the difference between a hexagon and a hexagram?

Hinge Theorem [12/12/2000]

How would you write a proof for the Hinge theorem?

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