
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 8th, 2012, 05:03 PM  #1  
Newbie Joined: Nov 2012 Posts: 4 Thanks: 0  Calculation of sides and area of rightangled trapezoid
I have to calculate sides and area of rightangled trapezoid if I know only diagonals. The task is: Quote:
(Sorry for my English, I am not from Englishspeaking country.)  
November 9th, 2012, 01:23 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Calculation of sides and area of rightangled trapezoid
Here is a sketch Triangles ABS, BCS and CDS are similar since angle BAS = angle CBS = angle DCS (see colored dots) and all these triangles are rightangled. So we have DS/CS = CS/BS = BS/AS (1), BS + DS = BD = 9 and AS + CS = AC = 12 Shifting AC a length of CD along CD gives us (CD + AB)^2 = 9^2 + 12^2 = 225. By Pythagoras: CS^2 + DS^2 = CD^2 CS^2 + BS^2 = BC^2 BS^2 + AS^2 = AB^2 AS^2 + DS^2 = AD^2 Now, let DS = a and CS/DS = b. Then CS = ab, BS = ab^2 and AS = ab^3. Gives us BS + DS = ab^2 + a = 9 = a(b^2 + 1) and AS + CS = ab^3 + ab = b(ab^2 + a) = 9b = 12 i.e. b = 4/3, so a = 9/(b^2 + 1) = 9/((4/3)^2 + 1) = 9/(5/3)^2 = 81/25. Can you use this to find the sides? 
November 9th, 2012, 06:56 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,802 Thanks: 2149 
I've corrected some slips in the above post.

November 10th, 2012, 04:26 AM  #4  
Newbie Joined: Nov 2012 Posts: 4 Thanks: 0  Re: Calculation of sides and area of rightangled trapezoid
Hello, thanks very much for your response. But I don't understand this: Quote:
 I was thinking about my solution, here it is: Let AB = a, BC = b, CD = c and DA = d. Then Code: d = ?((ac)²  b²) Code: a² + b² = 12² = 144 b² + c² = 9² = 81 Code: b² = 144  a² = 81  c² b² = a²  c² = 63 Code: a² + b² = 144 a² + 63 = 144 a² = 81 a = 9 Code: b² + c² = 81 63 + c² = 81 c² = 18 Next thing, if AS = x, CS = 12x, DS = y and BS = 9y then due to Pythagoras Code: a² = 12x b² = 9*(9y) = 12*(12x) c² = 9y Code: 12x = y(9y) 9y = x(12x) 12x  9y = x²  y² Code: c²  y² = a²  x² x²  y² = a² c² ... b² = a² c² Thanks very much.  
November 10th, 2012, 12:42 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,802 Thanks: 2149 
There's more than one error. If you try to justify everything you have done, you should be able to spot the errors.

November 10th, 2012, 12:50 PM  #6  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Calculation of sides and area of rightangled trapezoid Quote:
 
November 10th, 2012, 01:46 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,802 Thanks: 2149 
Both expressions are valid.

November 10th, 2012, 05:46 PM  #8  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Quote:
 
November 11th, 2012, 03:00 AM  #9  
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Quote:
Here is what I used: Earlier, we found: DS/CS = CS/BS = BS/AS which gives CS/DS = BS/CS = AS/BS I set DS = a and CS/DS = b, yields, CS = CS * 1 = CS * (DS/DS) = DS * (CS/DS) = a * b = ab. (you don't need the bold brackets..) Likewise, BS = CS * (BS/CS) = ab * b = ab^2 and AS = BS * (AS/BS) = ab^2 * b = ab^3 Get it? Quote:
 
November 11th, 2012, 08:29 AM  #10  
Global Moderator Joined: Dec 2006 Posts: 20,802 Thanks: 2149  Quote:
 

Tags 
area, calculation, rightangled, sides, trapezoid 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Finding Sides and area of trapezoid around two circles.  Spaghett  Algebra  16  June 30th, 2013 10:13 AM 
Area of Parallelogram and Trapezoid question?  nemsest  Calculus  5  March 19th, 2013 05:05 AM 
Finding altitude of a part of trapezoid with given area...  lei  Algebra  4  May 1st, 2012 03:57 AM 
Area of Triangles in Trapezoid  Spaghett  Algebra  4  June 18th, 2011 10:24 PM 
Det. length of sides of polygon from Area and ratio of sides  telltree  Algebra  0  January 21st, 2010 12:51 PM 