All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Polygon Overlap (Posted on 2017-04-17) Difficulty: 2 of 5

Side DE of square BCDE splits ΔABC into a smaller ΔAFG
and a quadrilateral BCGF. The area of ΔABC is twice that of
the square.

What is the value of Area(ΔAFG) / Area(BCGF) ?

No Solution Yet Submitted by Bractals    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution Comment 1 of 1
The height of triangle ABC from A to base BC is four times the side length of the square and thus four times the height of trapezoid BCGF from its top GF to its base BC.

Let's assume the square is a unit square so the triangle has base 1 and height 4. FG has length 3/4. The trapezoid BCGF therefore has area (1 + 3/4)*1/2 = 7/8, while the full triangle ABC has area 2, leaving 9/8 for the smaller triangle AFG.

The ratio asked for is then 9/7.

  Posted by Charlie on 2017-04-17 10:49:34
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information