Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 35, 58, and 41 units in length?

Answer 1

Area of triangle is `708.36` square units.

Explanation:

According to Heron's formula, if `a`, `b` and `c` are three sides of a triangle, its area is given by `sqrt(s(s-a)(s-b)(s-c))`, where `s=1/2(a+b+c)`.

The sides of triangle are `35`, `58` and `41` and hence

`s=1/2(35+58+41)=1/2xx134=67` and

Area of triangle is `sqrt(67xx(67-35)xx(67-58)xx(67-41))`

= `sqrt(67xx32xx9xx26)`

= `4xx3xxsqrt(67xx2xx26)=12sqrt3484=12xx59.03=708.36` square units.