Make up the lengths of three sides of a triangle and find its area using Heron's formula.

Question

anonymous · Answer

Heron's formula allows you to find the area of ANY triangle knowing only its sides. You don't need a height or anything. $$A = \sqrt{s(s-a)(s-b)(s-c)}$$ where s is the semi-perimeter, or half the perimeter of the triangle. You didn't include any side lengths, but the approach is pretty straight-forward. Find s = 1/2 ( a + b + c). And plug it into A. A derivation/proof of this formula can be found online. I prefer the one below as it includes every step. http://www.mathalino.com/reviewer/derivation-formulas/derivation-heron-s-hero-s-formula-area-triangle.

hero · Answer

a = 3
b = 5
c = 7

$$s = \frac{a + b + c}{2}$$
$$A = \sqrt{s(s-a)(s - b)(s - c)}$$

anonymous · Answer

wouldnt it be s = 1/2(a + b + c)?

anonymous · Answer

oops okay just saw @TurtleMuffin 's answer. thank you!!!