Geometry Area of Other Triangles
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That Area's Not Right
Area of Other Triangles

 

 That formula we had on the last page 

 works great when we have a right triangle.
 But what if we don't?
 
 What would we do with this puppy?
 

 

 
 First let's check and make sure 
 that it's not a right triangle ...
 Multiply the sides times themselves
 and see if the two smaller products
 add up to the product from the larger one.
 

 
 So fine, this is not a right triangle.
 Now what?
 To solve this one, we need another measurement.
 We need to know the distance from the side on the bottom
 straight up to the point of the angle on the top.
 

 

 
 The new line going straight up from the bottom,
 makes two right angles with the side on the bottom.
 

 

 Maybe you remember from the Zillion Names page, 
 that this new line is perpendicular to the line on the bottom.
 
 With the things we know how to do, 
 we can't calculate the length of this new line.
 Someday we'll be able to, 
 but for now somebody has to tell us what it is.
 
 OK, it's 12.

 

 
 Some people call this new line the "height" of the triangle.
 Some call it the "altitude" of the triangle.
 
 Anyway, whatever it is ... we got it.
  Now what?
 
 Now, just use the same formula !
 
 You're kidding?
 
 Nope, it works every time.
 

 

 
 Oh yeah?
 Works every time eh?
 How about this one ...
 

 

 
 Does the height on this puppy work like this?
 

 

 NO! NO! NO! NO! NO! NO! 

 
 To make this one work you have to flip the triangle over.
 

 

 
 The new line MUST start from inside the triangle at the bottom!
 

 

 
 Example:
 Figure out the area of this triangle ...
 

 

 

 

 
 Next Example:
 Find the area of this triangle ...

 

 
 To solve this one, we need to know the length of the base.
 This is a right triangle, so we know that the sum of 52
 plus the unknown side squared, equals 132.
 So:
  52 + base2 = 132
  25 + base2 = 169
  base2 = 144
  base = 12
 
 NOW WE'RE READY!
 

 

 

   copyright 2005 Bruce Kirkpatrick

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