Find the area of each triangle ABC.


a = 76.3 ft, b = 109 ft, c = 98.8 ft

Verified step by step guidance

1. Identify that you have a triangle with sides a = 76.3 ft, b = 109 ft, and c = 98.8 ft.
2. Recognize that you can use Heron's formula to find the area of the triangle, which is suitable when all three sides are known.
3. Calculate the semi-perimeter of the triangle using the formula: s = \frac{a + b + c}{2}.
4. Substitute the given side lengths into the semi-perimeter formula: s = \frac{76.3 + 109 + 98.8}{2}.
5. Use Heron's formula to find the area: \text{Area} = \sqrt{s(s-a)(s-b)(s-c)} and substitute the values of s, a, b, and c into the formula.

Key Concepts

Triangle Area Formula

The area of a triangle can be calculated using various formulas, one of which is Heron's formula. This formula is particularly useful when the lengths of all three sides are known. It states that the area A can be found using A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle, calculated as s = (a + b + c) / 2.

Semi-Perimeter

The semi-perimeter of a triangle is half the sum of its side lengths. It is a crucial component in Heron's formula for calculating the area. For triangle ABC with sides a, b, and c, the semi-perimeter s is computed as s = (a + b + c) / 2, which simplifies the area calculation by providing a single value to work with.

Heron's Formula

Heron's formula allows for the calculation of the area of a triangle when the lengths of all three sides are known. It is particularly advantageous because it does not require knowledge of the height or angles of the triangle. By substituting the side lengths into the formula A = √(s(s-a)(s-b)(s-c)), one can efficiently determine the area without additional geometric information.