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March 22nd, 2014, 09:56 PM  #1 
Senior Member Joined: Nov 2013 Posts: 247 Thanks: 2  Height unknown but need area.
I have a triangle with lengths 3.2, 3.8, and 2.4. I need the area but have to figure out the height because the triangle is not a right triangle. I would have 2 sides unknown if I just try to do the Pythagorean theorem. How can I figure out the height without doing the Pythagorean theorem if at all possible? Now since this is scalene would I get 3 different areas if I use the 3 different altitudes and bases? 
March 22nd, 2014, 10:06 PM  #2 
Senior Member Joined: Mar 2014 Posts: 112 Thanks: 8 
Heron's formula

March 22nd, 2014, 10:09 PM  #3 
Senior Member Joined: Mar 2014 Posts: 112 Thanks: 8 
Also, you could use the law of cosines and determine the angle to determine the height. My above post generally gives the area of a triangle.

March 23rd, 2014, 12:01 PM  #4  
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: Height unknown but need area. Quote:
 
March 23rd, 2014, 02:27 PM  #5  
Senior Member Joined: Nov 2013 Posts: 247 Thanks: 2  Re: Height unknown but need area. Quote:
Now if the Heron's formula works for triangles will it work for other polygons like quadrilaterals for example if you have 3,2,4,5 as sides of a quadrilateral (don't know if you would actually get a polygon but we will do with it) you have this: Would this be the actual area of a quadrilateral with sides 3, 2, 4, and 5?  
March 23rd, 2014, 03:18 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,978 Thanks: 2229 
In general, the area of a quadrilateral can't be determined from just the lengths of its sides (as quadrilaterals with the given sides but different areas would exist).

March 23rd, 2014, 03:45 PM  #7  
Senior Member Joined: Nov 2013 Posts: 247 Thanks: 2  Types of quadrilaterals Quote:
Concave Convex Tangential (externally tangent to a circle) Cyclic (internally tangent to a circle) Trapezoid Kite Rhomboid Rhombus Rectangle Oblong (used to mean rectangle that is not square) Square Parallelogram Right Trapezoid (1 right angle) Isosceles Trapezoid (at least 2 sides equal) 3 sides equal trapezoid (special case of Isosceles Trapezoid) Bicentric (internally and externally tangent to a circle) How can you figure out which of these types of quadrilaterals are possible with given side lengths? How would you find the area of a concave quadrilateral? Here is the hierarchy: Simple Inside that is convex and concave Inside convex is Tangential, Trapezoid, and Cyclic Inside Tangential is Kite and Bicentric Inside Trapezoid is Parallelogram, Right Trapezoid, and Isosceles Trapezoid Inside Cyclic is Isosceles Trapezoid and Bicentric Inside Kite is Rhombus Inside Parallelogram is Rectangle and Rhombus Inside Right Trapezoid is Rectangle Inside Isosceles Trapezoid is Rectangle and 3 Sides Equal Trapezoid Inside Rhombus, 3 Sides Equal Trapezoid, Bicentric, and Rectangle is Square  
March 23rd, 2014, 07:45 PM  #8 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: Height unknown but need area.
You can use Brahmagupta's Formula for cyclic quadrilaterals, which can be generalized for any noncyclic quadrilateral.

March 23rd, 2014, 11:18 PM  #9 
Newbie Joined: Mar 2014 Posts: 10 Thanks: 0  Re: Height unknown but need area.
Use Heron's formula for any triangle. ~Cheezees Fiverr.com/Cheezees 
March 24th, 2014, 09:00 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Height unknown but need area.
Fiverr.com/Cheezees http://www.fiverr.com/cheezees/doupto ... questions And you only charge 5 bucks? 

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