Question

How do you find the area of a triangle given a=3, b=7, c=8?

Answer 1

Use Heron's formula to find the area of the triangle = `6sqrt(3)`

Explanation:

Given three sides of a triangle: `a, b, c`
and the semi-perimeter `s = (a+b+c)/2`

Heron's formula says that the area of the triangle can be calculated as:
`color(white)("XXXX")` `A= sqrt(s(s-a)(s-b)(s-c))`

Given: `color(white)("XXXX")` `a=3` `color(white)("XXXX")` `b=7` `color(white)("XXXX")` `c=8`
`color(white)("XXXX")` `s=9`
and the area is
`color(white)("XXXX")` `A = sqrt(9*6*2*1)`
`color(white)("XXXX")` `color(white)("XXXX")` `=sqrt(108)`
`color(white)("XXXX")` `color(white)("XXXX")` `=6sqrt(3)`