How to Find the Area of a Triangle, with some Examples

To Find the Area of a Triangle is relatively easy if the Height and the Base of the Triangle are known. since there is a well known Formula that states... Area of a Triangle is equal to one-half of the Product of the Base and the Height. If the Base and the Height are not known then we have a very interesting and challenging situation. This Article will give some Examples of How to Find those Areas.

Things You'll Need

• Paper and
• Pencil

Instructions

1. 

   The Area of a Right Triangle, with the Lengths of the 2 perpendicular sides given, and labeling one of the perpendicular side as the Base and the other perperdicular side as the height the Area can be found by the following formula: Area = ( Base x Height) / 2. Click on the Image for a better understanding.

2. 

   If the Triangle is an Equilateral Triangle and the Length of one of its sides is known, the Area fo this Triangle can be found by the following Formula: Area = [ √3 ( side )² ] /4 and the Height = [ √3 ( side ) ] / 2. Click on the image for a better understanding.

3. 

   If the Triangle is an Isoseles Triangle and the Length of the base is known and the length of one of the other sides is known then the area can be found by the following formula: Area = [ ( Base √ (4 side² - base²) ] / 4. Click on the Image for a better understanding.

4. 

   If the Triangle is a Scalene Triangle (no two sides are equal to each other) and the lengths of all three sides are known we use the formula called Zeno's formula: Area = √ [s(s - a)(s - b)(s - c)], where s = half the perimeter of the Triangle and a, b, and c are the respective lengths of each of the sides of the Triangle. Click on the image for a better understanding.

5. Depending on the Triangle given, there are many different ways or methods to find the Area of a Triangle: using Trigonnometry, using determinants, using cross products in vector analysis, etc.

Resources

• Read this Article in Spanish