How to Calculate the Area of a Triangle

Step-by-Step Guide

1. 1

   Step 1: Find the base and height of the triangle.

   The base is one side of the triangle.
   
   The height is the measure of the tallest point on a triangle.
   
   It is found by drawing a perpendicular line from the base to the opposite vertex.
   
   This information should be given to you, or you should be able to measure the lengths.
   
   For example, you might have a triangle with a base measuring 5 cm long, and a height measuring 3 cm long.
2. 2

   Step 2: Set up the formula for the area of a triangle.

   The formula is Area=12(bh){\displaystyle {\text{Area}}={\frac {1}{2}}(bh)}, where b{\displaystyle b} is the length of the triangle’s base, and h{\displaystyle h} is the height of the triangle., Multiply the two values together, then multiply their product by 12{\displaystyle {\frac {1}{2}}}.
   
   This will give you the area of the triangle in square units.
   
   For example, if the base of your triangle is 5 cm and the height is 3 cm, you would calculate:
   Area=12(bh){\displaystyle {\text{Area}}={\frac {1}{2}}(bh)}Area=12(5)(3){\displaystyle {\text{Area}}={\frac {1}{2}}(5)(3)}Area=12(15){\displaystyle {\text{Area}}={\frac {1}{2}}(15)}Area=7.5{\displaystyle {\text{Area}}=7.5} So, the area of a triangle with a base of 5 cm and a height of 3 cm is
   7.5 square centimeters. , Since two sides of a right triangle are perpendicular, one of the perpendicular sides will be the height of the triangle.
   
   The other side will be the base.
   
   So, even if the height and/or base is unstated, you are given them if you know the side lengths.
   
   Thus you can use the Area=12(bh){\displaystyle {\text{Area}}={\frac {1}{2}}(bh)} formula to find the area.
   
   You can also use this formula if you know one side length, plus the length of the hypotenuse.
   
   The hypotenuse is the longest side of a right triangle and is opposite the right angle.
   
   Remember that you can find a missing side length of a right triangle using the Pythagorean Theorem (a2+b2=c2{\displaystyle a^{2}+b^{2}=c^{2}}).
   
   For example, if the hypotenuse of a triangle is side c, the height and base would be the other two sides (a and b).
   
   If you know that the hypotenuse is 5 cm, and the base is 4 cm, use the Pythagorean theorem to find the height:a2+b2=c2{\displaystyle a^{2}+b^{2}=c^{2}}a2+42=52{\displaystyle a^{2}+4^{2}=5^{2}}a2+16=25{\displaystyle a^{2}+16=25}a2+16−16=25−16{\displaystyle a^{2}+16-16=25-16}a2=9{\displaystyle a^{2}=9}a=3{\displaystyle a=3}Now, you can plug the two perpendicular sides (a and b) into the area formula, substituting for the base and height:
   Area=12(bh){\displaystyle {\text{Area}}={\frac {1}{2}}(bh)}Area=12(4)(3){\displaystyle {\text{Area}}={\frac {1}{2}}(4)(3)}Area=12(12){\displaystyle {\text{Area}}={\frac {1}{2}}(12)}Area=6{\displaystyle {\text{Area}}=6}
3. 3

   Step 3: Plug the base and height into the formula.

4. 4

   Step 4: Find the area of a right triangle.

Detailed Guide

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