This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the semi-perimeter s of the triangle. The side lengths are a = 10 cm, b = 13 cm, and c = 8 cm. s = (a+b+c)/(2) s = (10 + 13 + 8)/(2) s = (31)/(2) s = 15.5 cm Step 2: Apply Heron's formula to find the area of triangle ABC. Heron's formula is given by: A = sqrt(s(s-a)(s-b)(s-c)) Substitute the values of s, a, b, and c: A = sqrt(15.5(15.5-10)(15.5-13)(15.5-8)) A = sqrt(15.5(5.5)(2.5)(7.5)) Step 3: Calculate the product inside the square root. A = sqrt(15.5 × 5.5 × 2.5 × 7.5) A = sqrt(1598.4375) Step 4: Calculate the square root to find the area. A ≈ 39.98046 Rounding to two decimal places: A ≈ 39.98 cm^2 The area of triangle ABC is: 39.98 cm^2 Send me the next one 📸