Question

A triangle has sides with lengths: 3, 2, and 4. How do you find the area of the triangle using Heron's formula?

Answer 1

Area `= 3/4sqrt(15)`

Explanation:

Given a triangle with sides `a, b, c`
and semiperimeter `s (=(a+b+c)/2)`

Heron's formula tells us that the area is:
`color(white)("XXX")"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))`

Using the given values `(a,b,c)=(3,2,4)`
`color(white)("XXX")s=9/2`
and
`color(white)("XXX")"Area"_triangle = sqrt((9/2)(3/2)(5/2)(1/2))`

`color(white)("XXX")=sqrt(135)/4`

`color(white)("XXX")=(3sqrt(15))/4`