Heron's Formula - Example | Don't Memorise

TL;DR

Learn how to use the Heron formula to calculate the area of a triangle when only the side lengths are given.

Transcript

consider a triangle pqr with sides 25 39 and 56 units how do we find the area of this triangle we don't have the height or the base but we have been given the length of all three sides since we've been given only the length of the sides we know we have to use the herin formula and to use the formula we need the semi parameter of the triangle let's ... Read More

Key Insights

• 🔺 The Heron formula provides a method to find the area of a triangle when only the side lengths are given.
• ❓ Calculating the semi-parameter is essential in using the Heron formula.
• 🌥️ Large numbers in the calculations can be simplified using the prime factorization method.
• 🇦🇪 The units of the area of a triangle are squared units.

Questions & Answers

Q: How do we find the area of a triangle when only the side lengths are given?

To find the area of a triangle with only the side lengths known, we can use the Heron formula, which involves calculating the semi-parameter and plugging the values into the formula.

Q: What is the semi-parameter of a triangle?

The semi-parameter (s) of a triangle is determined by dividing the sum of all three side lengths by 2. It is an important value required in the Heron formula to calculate the area of the triangle.

Q: Why is it not recommended to multiply the large numbers when finding the area using the Heron formula?

Large numbers can create difficult calculations and the risk of errors. Instead, it is suggested to use the prime factorization method to simplify the square roots and make the calculations more manageable.

Q: How can the prime factorization method be used to find the square root of large numbers?

By breaking down the numbers into their prime factors and grouping them together, we can simplify the square root calculation. From each group, we select one number, multiply them together, and remove the square root sign.

Summary & Key Takeaways

• The Heron formula is used to find the area of a triangle when the lengths of all three sides are provided.

• The semi-parameter (s) of the triangle is calculated by dividing the sum of all three sides by 2.

• The area of the triangle can be calculated using the Heron formula: √(s * (s - a) * (s - b) * (s - c)), where a, b, and c are the side lengths.