10981
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
Ratios of the Areas of an Internal Hexagon to Its Star to the External Hexagon
Abraham Gadalla
Areas of Parallelograms and Trapezoids
Helen Papadopoulos
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+