9853
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Ratio of Areas in a Square
Given: a square
with side length
and diagonal
. Place point
on
and let
. Connect
to divide the square into four areas. Given
, calculate the ratio of areas. For example, let
.
Contributed by:
Abraham Gadalla
THINGS TO TRY
Drag Locators
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
The key here is that the height of
equals the height of
, so the ratio of the areas between those two triangles is
.
Hence,
.
Similarly, comparing areas,
. Therefore |
.
Substituting gives
.
At this point, one can calculate the height
of
as
.
Then
and
.
Also,
.
After simplification, the ratio of the four areas is:
.
RELATED LINKS
Ratio
(
Wolfram
MathWorld
)
PERMANENT CITATION
Abraham Gadalla
"
Ratio of Areas in a Square
"
http://demonstrations.wolfram.com/RatioOfAreasInASquare/
Wolfram Demonstrations Project
Published: August 15, 2011
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
The Area of a Square in a Square
Abraham Gadalla
Total Areas of Alternating Subtriangles in a 2n-gon
Jay Warendorff
Isosceles Trapezoid Area
Michael Schreiber
Signed Area of a Polygon
Bruce Atwood (Beloit College) and Stan Wagon (Macalester College)
Area of a Quadrilateral by Triangulation
Alvaro Jose Ibarra Rivas (Institucion Educativa Santa Fe, Santiago de Cali - Colombia)
Area of a Hexagon Formed by the Vertices and Altitude Extensions of a Triangle
Jay Warendorff
The Excentral Triangle and a Related Hexagon
Jay Warendorff
Equilateral Triangles That Form a Star
Rik Agosti
Areas of Parallelograms and Trapezoids
Helen Papadopoulos
A Relation between the Areas of Four Triangles
Jay Warendorff
Related Topics
Area
Plane Geometry
Polygons
Triangles
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+