HERONS FORMULA

Front

What is Heron's Formula?

Back

Heron's Formula is a method for calculating the area of a triangle when the lengths of all three sides are known. It states that the area (A) can be calculated using the formula: A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle, calculated as s = (a+b+c)/2.

Front

How do you calculate the semi-perimeter of a triangle?

Back

The semi-perimeter (s) of a triangle is calculated by adding the lengths of all three sides (a, b, c) and dividing by 2: s = (a + b + c) / 2.

Front

What is the area of a triangle with sides 3 cm, 4 cm, and 5 cm using Heron's Formula?

Back

First, calculate the semi-perimeter: s = (3 + 4 + 5) / 2 = 6. Then, apply Heron's Formula: A = √(6(6-3)(6-4)(6-5)) = √(6 * 3 * 2 * 1) = √(36) = 6 cm².

Front

What is the area of an equilateral triangle with side length 6 cm?

Back

For an equilateral triangle, the area can be calculated using the formula: A = (√3/4) * a². Thus, A = (√3/4) * 6² = (√3/4) * 36 = 9√3 cm².

Front

If a triangle has sides of lengths 7 cm, 8 cm, and 9 cm, what is its area?

Back

First, calculate the semi-perimeter: s = (7 + 8 + 9) / 2 = 12. Then, apply Heron's Formula: A = √(12(12-7)(12-8)(12-9)) = √(12 * 5 * 4 * 3) = √(720) = 12√5 cm².

Front

What is the significance of Heron's Formula in geometry?

Back

Heron's Formula is significant because it allows for the calculation of the area of a triangle without needing to know the height, making it useful for various applications in geometry and trigonometry.

Front

How can you verify the area calculated using Heron's Formula?

Back

You can verify the area by comparing it with the area calculated using the base-height formula (A = 1/2 * base * height) if the height can be determined.

Front

What is the area of a triangle with sides 5 cm, 12 cm, and 13 cm?

Back

First, calculate the semi-perimeter: s = (5 + 12 + 13) / 2 = 15. Then, apply Heron's Formula: A = √(15(15-5)(15-12)(15-13)) = √(15 * 10 * 3 * 2) = √(900) = 30 cm².

Front

What happens if the triangle is degenerate (i.e., the sum of two sides equals the third)?

Back

If a triangle is degenerate, the area calculated using Heron's Formula will be zero, as the triangle collapses into a straight line.

Front

Can Heron's Formula be used for non-integer side lengths?

Back

Yes, Heron's Formula can be used for any positive real numbers as side lengths, not just integers.