My Math Forum  

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

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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?
caters is offline  
 
March 22nd, 2014, 10:06 PM   #2
Senior Member
 
Joined: Mar 2014

Posts: 112
Thanks: 8

Heron's formula
the john is offline  
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.
the john is offline  
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:
Originally Posted by caters
Now since this is scalene would I get 3 different areas...
It's the same triangle, isn't it, so why would the area change? The height and the base are inversely proportional, so if the height increases, the base decreases. The easiest way is to use Heron's formula, as the john has said
eddybob123 is offline  
March 23rd, 2014, 02:27 PM   #5
Senior Member
 
Joined: Nov 2013

Posts: 247
Thanks: 2

Re: Height unknown but need area.

Quote:
Originally Posted by eddybob123
Quote:
Originally Posted by caters
Now since this is scalene would I get 3 different areas...
It's the same triangle, isn't it, so why would the area change? The height and the base are inversely proportional, so if the height increases, the base decreases. The easiest way is to use Heron's formula, as the john has said
Yeah it is but you could use the law of sines, law of cosines, or law of tangents to figure out the angle and than figure out the height from sides + angles and than use 1/2 b * h to figure out the area.

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?
caters is offline  
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).
skipjack is offline  
March 23rd, 2014, 03:45 PM   #7
Senior Member
 
Joined: Nov 2013

Posts: 247
Thanks: 2

Types of quadrilaterals

Quote:
Originally Posted by skipjack
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).
Here is a list of the types of quadrilaterals:
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
caters is offline  
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 non-cyclic quadrilateral.
eddybob123 is offline  
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
Cheezees is offline  
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/do-up-to ... -questions

And you only charge 5 bucks?
Denis is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
area, height, unknown



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
x^e mod P where x is unknown zxcvbnm123 Number Theory 1 February 19th, 2014 01:26 AM
find area with perimeter and height giorgal2 Algebra 4 October 13th, 2012 05:14 AM
Area of a segment of a circle from % of height. fishinmyi Algebra 6 October 27th, 2011 09:34 AM
Finding unknown value from area jsmith613 Calculus 7 November 15th, 2010 01:57 AM
reduce area, calculate new height,width hahaha Algebra 7 November 12th, 2007 09:38 AM





Copyright © 2019 My Math Forum. All rights reserved.