# What is the area of a triangle with sides of length 1, 2, and 2?

$A r e a = \frac{\sqrt{15}}{4}$ square units

#### Explanation:

Use the Heron's formula

Area=sqrt(s*(s-a)(s-b)(s-c)

Let $a = 2 , b = 2 , c = 1$

compute $s$

$s = \frac{1}{2} \left(a + b + c\right) = \frac{1}{2} \cdot \left(2 + 2 + 1\right) = \frac{5}{2}$

Now, compute the Area

Area=sqrt(s*(s-a)(s-b)(s-c)

Area=sqrt(5/2*(5/2-2)(5/2-2)(5/2-1)

$A r e a = \sqrt{\frac{5}{2} \cdot \left(\frac{1}{2}\right) \left(\frac{1}{2}\right) \left(\frac{3}{2}\right)} = \sqrt{\frac{15}{16}} = \frac{\sqrt{15}}{4}$