Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `23`, `21`, and `20`?

Answer 1

Find the semiperimeter first then use Heron's formula
Area is `24sqrt(66)`

Explanation:

Heron's formula states that
Area = `sqrt(s(s-a)(s-b)(s-c))`

Where s is the sum of all sides / 2 (Also known as the semiperimeter)
a,b,c are the side lengths

From here, you can just plug in all the values.
Find that s = 32
Area = `sqrt(32(9)(11)(12))`
prime factorize the inside to get `sqrt((2^7)(3^3)(11))`

Then take out the squares to get
`2^3 * 3` `sqrt(2*3*11)`
Finally
`24sqrt(66)`