See also the
Dr. Math FAQ:
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.
Pythagorean theorem proofs.
- Area and Perimeter: Mowing the Lawn [6/1/1996]
How many circuits are necessary to cut half the lawn?
- Are All Triangles Isosceles? [09/15/1999]
Can you help me find the flaw in this 'proof' claiming that all triangles
- Area of a Half-Mowed Yard [08/21/2003]
There is a square/rectangular yard, size unknown. You have mowed a 10
foot swath around the perimeter. You are now half done. How big is
- Area of a Hexagon [7/9/1996]
How do you calculate the area of a hexagon?
- Area of a Lawn [09/04/2002]
I have two areas of lawn that I want to sod with new grass and don't
know how much sod to buy.
- Area of an Inscribed Quadrilateral [05/11/2000]
Given a quadrilateral where the midpoints of each side are connected to
form a new quadrilaterals inside the first, what is the ratio of the area
of the larger quadrilateral to the smaller one?
- Area of an Irregular Polygon Given Side Length [8/2/1996]
What is the area of an irregular quadrilateral with side lengths in a
clockwise order of 43.61, 133.64, 146.96, and 110.85?
- Area of an Octagonal House [08/24/2003]
I plan to build an octagonal home, and would like to know the area of
the completed home if each wall span is 14 feet in length.
- Area of an Unspecified Triangle [6/1/1996]
A square ABCD, with side "y", and an equilateral triangle DEF, with the
same side "y", are in contact at point "d"...
- Area of an Unusual Hexagon [12/05/1996]
Find the area of a hexagon made from a triangle with squares appended to
each of its sides and three more triangles each consisting of one unknown
side and two sides which are shared with two of the squares.
- Area of a Polygon [06/27/1997]
If you know the coordinates of the vertices, how do you calculate the
area of a polygon?
- Area of a Rectangle Outside a Rectangle [6/11/1996]
Find the area of the concrete border of a rectangular swimming pool.
- Area of a Regular Octagon [10/27/1999]
How do you find the area of a regular octagon?
- Area of a Regular Octagon: Proof of a Formula [08/31/1998]
A proof of the formula.
- Area of a Rhombus and Area of a Square [11/16/2007]
A rhombus has four equal sides, so it's a 'pushed over' square. Why is
the area formula not side times side like in a square?
- Area of a Right Triangle [02/09/2002]
Find the area of a right triangle that has a perimeter of length 16
meters and a hypotenuse with length 7 meters.
- The Area of a Roof [05/18/2002]
How can I determine the area of a hipped roof for a building 100
feet long and 80 feet wide, with a pitch of 6/12, and 3 feet of
overhang for the eaves?
- The Area of a Square Inscribed in a Circle [12/23/1995]
What is the area of a square inscribed in a circle whose circumference is
- Area of a Trapezoid [04/27/1997]
Find the area of a trapezoid with three sides of length 80 and one of
- Area of a Triangle [6/2/1996]
Knowing one side measures 1 and two adjacent angles measure a and b...
- Area of Bermuda Triangle [06/10/2001]
The Bermuda triangle is shown on a graph with the points A(1,2) B(4,8)
and C(8,1). Determine the area of the triangle two different ways.
- Area of Equilateral Triangle [12/06/2002]
Equilateral triangle ABC has, near its center, point P, which is 3,
4, and 5 units from the three vertices. What is the area of triangle
- Area of Inscribed Circle [12/01/1998]
Find the area of the circle inscribed in a triangle ABC using Heron's
- Area of Polygon [08/20/1999]
Using coordinate system to find the areas of polygons.
- Area of Quadrilateral, Given Angles and Two Opposite Sides [05/13/2002]
If I have a quadrilateral with all the angles known and two opposite
sides known, can I find the area?
- Area of Trapezoid Given Only the Side Lengths [12/15/2008]
How do you find the area of a trapezoid if all you are given is the
four side lengths and you don't know which pair of sides is parallel?
- The Area of Triangles using Hero's Formula [12/13/1995]
If a person gave three dimensions of a triangle (in feet) and noted the
base dimension, without knowing the angles because the other two lines
would have to intersect someplace, is there a formula that could
calculate the area?
- Area of Triangles When Altitudes Are Given [12/16/2002]
Find the area of a triangle when the lengths of the three altitudes
- Area, Perimeter, and Congruency of Quadrilaterals [06/23/2003]
I'm trying to find out how to prove or disprove if it is always true
that if two quadrilaterals have the same area and the same perimeter,
they will always be congruent.
- Areas of N-Sided Regular Polygon and Circle [02/24/2005]
The area of an n-sided regular polygon approaches the area of a circle
as n gets very large.
- Attempt at Trisecting an Angle [11/08/1999]
Can the arcs of the two circles formed by the construction described be
the same length? Would this construction trisect the angle?
- Axes of Symmetry [2/3/1996]
Can you help a year 5 student understand axes of symmetry of a triangle?
- Base or Width? [06/11/2002]
When computing area, is there a difference between 'width' and 'base'?
- Bounding Rectangle for an Ellipse [6/28/1996]
I would like to know if there is a general equation for a bounding
rectangle of an ellipse.
- Break a dowel to form a triangle [3/8/1995]
A wooden dowel is randomly broken in 2 places. What is the probability
that the 3 resulting fragments can be used to form the sides of a
- Broken Flag Pole [9/11/1996]
A 90 ft high flag pole sits atop and in the corner of a 10 ft high, 10 ft
wide building. The pole breaks...
- Building a Cone [10/28/2001]
I am trying to find a formula for building a cone for a chimney flashing.
It should be 21" tall with a top opening of 8", a bottom opening of 20",
and a vertical seam overlap of 2".
- Building a Skateboard Ramp [9/19/1995]
I'm trying to build a skateboard ramp, pyramid with flat top, height one
foot, angle of ascent thirty degrees, other angles ninety degrees and
- Building Squares with Tangram Puzzle Pieces [03/21/2006]
Is it possible to build a square using only 6 of the 7 pieces of the
well-known Tangram puzzle?
- Calculating Areas of Quadrilaterals and Triangles [08/30/2005]
What portion of an acre is a plot of land that is 85 x 174 x 73 x 118?
How about a plot of land that is 150 x 118 x 150?