Question

A triangle has sides with lengths: 16, 8, and 19. How do you find the area of the triangle using Heron's formula?

Answer 1

(see below for method)
Approximate area `63.2`

Explanation:

Heron's Formula tells us that if we are given a triangle with sides `a, b, c` and a semi-perimeter `s=(a+b+c)/2`, the area of the triangle is:
`color(white)("XXX")"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))`

For the given values `(a,b,c)=(16,8,19)`
`color(white)("XXX")s=43/2`

`color(white)("XXX")(s-a)=11/2`
`color(white)("XXX")(s-b)=27/2`
`color(white)("XXX")(s-c)=5/2`

Applying the formula (and using a calculator)
`color(white)("XXX")"Area"_triangle ~~63.2`