Heron's Formula

Front

What is Heron's Formula?

Back

Heron's Formula is a mathematical formula used to calculate the area of a triangle when the lengths of all three sides are known. It is given by the formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle, and a, b, and c are the lengths of the sides.

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How do you calculate the semiperimeter of a triangle?

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

Front

If a triangle has sides of lengths 7, 8, and 9, what is the semiperimeter?

Back

The semiperimeter s = (7 + 8 + 9) / 2 = 12.

Front

Using Heron's Formula, find the area of a triangle with sides 7, 8, and 9.

Back

First, calculate the semiperimeter: s = (7 + 8 + 9) / 2 = 12. Then, Area = √(12(12-7)(12-8)(12-9)) = √(12 * 5 * 4 * 3) = √720 = 26.83.

Front

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

Back

Heron's Formula 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 real-world problems.

Front

What are the conditions for using Heron's Formula?

Back

Heron's Formula can be used for any triangle as long as the lengths of all three sides are known and they satisfy the triangle inequality theorem.

Front

What is the triangle inequality theorem?

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The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If a triangle has sides of lengths 10, 14, and 16, what is the area using Heron's Formula?

Back

First, calculate the semiperimeter: s = (10 + 14 + 16) / 2 = 20. Then, Area = √(20(20-10)(20-14)(20-16)) = √(20 * 10 * 6 * 4) = √4800 = 69.28.

Front

What is the formula for the area of a triangle using base and height?

Back

The area of a triangle can also be calculated using the formula: Area = (1/2) * base * height.

Front

How does Heron's Formula compare to the base-height formula?

Back

Heron's Formula is useful when the height of the triangle is unknown, while the base-height formula requires knowledge of the base and the corresponding height.