What is the formula for calculating the area of a scalene triangle?

What is the formula for calculating the area of a scalene triangle?

The area of a scalene triangle can be calculated using Heron's formula. First, you need to find the semi-perimeter (s) of the triangle, which is given by s = (a + b + c) / 2, where a, b, and c are the lengths of the sides. Then, the area (A) can be calculated as A = √(s(s-a)(s-b)(s-c)).

Can you give me an example using specific side lengths?

Sure! Let's say the sides of the scalene triangle are 5, 6, and 7 units. First, calculate the semi-perimeter: s = (5 + 6 + 7) / 2 = 9. Then, apply Heron's formula: A = √(9(9-5)(9-6)(9-7)) = √(9 * 4 * 3 * 2) = √(216) ≈ 14.7 square units.

What if I only know the height and base?

If you know the height and base of the scalene triangle, you can use the formula: Area = (base * height) / 2. This works for any triangle, including scalene.

Are there other methods to find the area?

Yes, besides Heron's formula and the base-height method, you can also use trigonometric methods if you know two sides and the included angle.