Area of a Triangle

Where:
B = Base of Triangle
H = Height of Triangle

A triangle's area tells us how big the triangle is. To calculate this, you must know the base of the triangle and its height. For help calculating a triangle's height, click here.

How Does the Equation Work?
A triangle is half of a parallelogram (a slanted square or rectangle.) To calculate the area of a parallelogram, you use the equation:

B * H

Therefore, since a triangle's area is half of its parallelogram's area, you find the area of its parallelogram and take half of that by dividing it by 2.

What About Heron's Formula?
If you know the three sides of the triangle you need the area of, you can use Heron's Formula. This way, you don't have to calculate the triangle's height if you don't already have it. Click the link above for this calculator and its help file.

How Can This Formula Be Used Outside of Math Class?
"Who really cares about triangles and how big they are in real life?" you're asking. Well, I have a few answers for you.

Say a building company is plotting the land on which it is going to build a playground. The swings of the playground will be in a separate, triangular area away from the other playground equipment. The school is requesting that mulch be used only in this area. To know how much mulch to use to cover the triangular area, the builders need to know the area of the triangle.

How about a painter who needs to know how much paint to use to cover a side of a staircase? If he/she knows the area of the triangle that the stairs and corner of the wall create, he won't buy too much or too little paint.

Someone writing a report on the Bermuda Triangle or the Polynesian Triangle might want to include in his/her paper how many miles these geographical areas cover.

If someone drew two triangles and used optical illusion to make them look like the same size, a curious witness may want to ease his/her mind by calculating which one is actually larger.

I'm sure there are plenty more instances; this just shows you that the equation for the area of a triangle isn't just another "pointless math equation" that you don't really need to know.

Example
Given a triangle's base is 3.6 inches and its height is 9 inches, what is its area?

Another Way of Finding a Triangle's Area
There is yet another way to find the area of a triangle. I won't go much into it in this help file because our calculator uses the equation I've been explaining thus far.

If you know two sides of your triangle and the angle in-between them, you can use Sine to find its area.

So, if you're told the angle of C in this triangle and sides a and b, you can use our Sine calculator to tell you what the Sine of angle C is and then multiply that by a * b to get your answer.

Related Websites:
http://www.ajdesigner.com/phptriangle/scalene_triangle_area_height.php
http://www.mste.uiuc.edu/dildine/heron/triarea.html
http://en.wikipedia.org/wiki/Triangle

Works Cited
Glosser, Gisele. "Area of Triangle." Mrs. Glosser's Math Goodies. 1998. Gisele
     Glosser. 15 June 2006. <http://www.mathgoodies.com/lessons/vol1/area_triangle.html>.

"Calculating the Area of a Triangle." Bradco Supply/Wickes Lumber. 2006. Bradco
     Supply Corporation. 15 June 2006. <http://www.bradcosupply.com/lumber_math.aspx>