# A triangle has sides with lengths: 6, 1, and 5. How do you find the area of the triangle using Heron's formula?

##### 1 Answer

Jan 25, 2016

First, find the **semiperimeter**

#### Explanation:

**Heron's Area**

**Area**

**Why is the area 0?**

The **Triangle Inequality Theorem** states that the length of any side of a triangle **MUST be less than** the sum of the other two sides. For this problem, the theorem **fails the test** :

**is not less than**

So, a triangle with sides 6, 1 and 5 is not a triangle!

hope that helped