How do you use Heron's formula to find the area of a triangle with sides of lengths 7 , 8 , and 8 ?

Feb 14, 2016

The area is approximately $A \approx 25.18$

Explanation:

Heron's formula says that for any triangle 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 for this example we have:

$p = \frac{7 + 8 + 8}{2} = \frac{23}{2} = 11.5$

$p - a = 11.5 - 7 = 4.5$

$p - b = p - c = 11.5 - 8 = 3.5$

so the area is:

$A = \sqrt{11.5 \cdot 4.5 \cdot 3.5 \cdot 3.5}$

$A = \sqrt{633.9379}$

$A \approx 25.18$