# How do you use Heron's formula to find the area of a triangle with sides of lengths 4 , 6 , and 5 ?

##### 1 Answer
Jan 29, 2016

The area is:

$A \approx 9.92$ square units

#### Explanation:

The Heron's Formula says that for any triangle with sides $a , b$ and $c$ its area can be calculated as:

$A = \sqrt{p \left(p - a\right) \left(p - b\right) \left(p - c\right)}$

where:

$p = \frac{a + b + c}{2}$.

So to calculate the area we calculate:

$p = \frac{4 + 5 + 6}{2} = 7.5$

$p - a = 7.5 - 4 = 3.5$

$p - b = 7.5 - 5 = 2.5$

$p - c = 7.5 - 6 = 1.5$

Now we can write that:

$A = \sqrt{7.5 \cdot 3.5 \cdot 2.5 \cdot 1.5}$

$A = \sqrt{98.4375}$

$A \approx 9.92$

Answer: The area is approximately $9.92$ square units