What are some examples of Heron's formula in action?

Can you explain Heron's formula and give me some examples?

Sure! Heron's formula is used to calculate the area of a triangle when you know the lengths of all three sides. The formula is: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle, calculated as (a+b+c)/2.

Can you provide a specific example using Heron's formula?

Absolutely! Let's say we have a triangle with sides of lengths 5, 6, and 7. First, we calculate the semi-perimeter: s = (5+6+7)/2 = 9. Then, we apply Heron's formula: Area = √(9(9-5)(9-6)(9-7)) = √(943*2) = √(216) ≈ 14.7 square units.

What if the sides were different, like 8, 15, and 17?

For sides 8, 15, and 17, the semi-perimeter is s = (8+15+17)/2 = 20. Using Heron's formula: Area = √(20(20-8)(20-15)(20-17)) = √(20125*3) = √(3600) = 60 square units.

Can Heron's formula be used for any triangle?

Yes, Heron's formula can be used for any triangle as long as you know the lengths of all three sides. It's particularly useful when you don't have the height of the triangle.