
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 12th, 2016, 04:08 PM  #1 
Newbie Joined: Dec 2016 From: United States Posts: 1 Thanks: 0  Area of a Quadrilateral vs. Area of a Kite
In my recent quiz I was told to find the area of the given quadrilateral. It had three given sides: 12, 9, 16. The angle between the sides lengths 12 and 9 was 90 degrees. The angle between the sides lengths 9 and 16 was 126 degrees. To find the area, I used the formula for a kite. To find the diagonals, I used the pythagorean theorem for the diagonal that forms the hypotenuse of the triangle with the right angle and I used the law of cosines to find the diagonal opposite the angle of 126 degrees. Then, i used the formula for area of a kite ((1/2)d1•d2). I got the correct answer (exactly) but the problem is that the quadrilateral is NOT a kite. How did I get the right answer?? The quadrilateral is definitely not a kite but i still got the right answer using the formula for area of a kite.

December 12th, 2016, 04:43 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,105 Thanks: 981 
the two methods of finding the area are close, but not exact ... using the diagonals, $d_1=15$, $d_2=\sqrt{9^2+16^22 \cdot 9 \cdot 16 \cdot \cos(126)}$, A = 168.7553587 using two triangles (the 91215 and the 1516 with the angle $\theta = 126\arctan(4/3)$ between them) ... A = 168.6766078 (the true area) both round to 169 I imagine they are close because the diagonals are close to being perpendicular 

Tags 
area, kite, law of cosines, quadrilateral, right angle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Area of a quadrilateral?  Tangeton  Geometry  8  February 24th, 2016 11:50 AM 
Area of a quadrilateral  shankarathreya  New Users  3  July 2nd, 2014 10:38 AM 
area of quadrilateral  panky  Algebra  2  December 18th, 2011 09:39 PM 
quadrilateral and area  michary91  Algebra  2  September 29th, 2010 04:34 AM 
quadrilateral area proof  meph1st0pheles  Algebra  4  February 25th, 2010 11:40 AM 