My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum

Thanks Tree2Thanks
  • 2 Post By skeeter
LinkBack Thread Tools Display Modes
December 12th, 2016, 03:08 PM   #1
Joined: Dec 2016
From: United States

Posts: 1
Thanks: 0

Question 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.
olivia1 is offline  
December 12th, 2016, 03:43 PM   #2
Math Team
Joined: Jul 2011
From: Texas

Posts: 2,611
Thanks: 1295

the two methods of finding the area are close, but not exact ...

using the diagonals, $d_1=15$, $d_2=\sqrt{9^2+16^2-2 \cdot 9 \cdot 16 \cdot \cos(126)}$, A = 168.7553587

using two triangles (the 9-12-15 and the 15-16 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
Thanks from topsquark and olivia1
skeeter is offline  

  My Math Forum > High School Math Forum > Geometry

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 10:50 AM
Area of a quadrilateral shankarathreya New Users 3 July 2nd, 2014 10:38 AM
area of quadrilateral panky Algebra 2 December 18th, 2011 08:39 PM
quadrilateral and area michary91 Algebra 2 September 29th, 2010 04:34 AM
quadrilateral area proof meph1st0pheles Algebra 4 February 25th, 2010 10:40 AM

Copyright © 2017 My Math Forum. All rights reserved.