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Heron's Formula Calculator, a powerful tool for calculating the area of a triangle without needing the height. Heron's Formula, named after the Hero of Alexandria, is particularly useful when the lengths of all three sides of a triangle are known. This calculator simplifies the process, providing quick and accurate results for any triangle.

Heron's Formula is a mathematical formula for finding the area of a triangle when the lengths of all three sides are known. Our calculator streamlines this process, making complex calculations effortless and error-free.

Heron's Formula is crucial in geometry, especially when dealing with triangles in real-world applications like architecture and physics. It offers an alternative approach to finding the area when the height is challenging to determine.

This calculator is handy when you have the lengths of all three sides of a triangle and need a quick solution for its area. It's applicable in scenarios where traditional methods involving height are impractical.

Heron's Formula is applicable in various fields such as construction, engineering, and navigation, where calculating the area of a triangle with known side lengths is essential for accurate planning and design.

Simply enter the lengths of the three sides of the triangle into the calculator, and it will use Heron's Formula to compute the area, providing you with instant results.

Heron's Formula is given by:

`Area =$\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})}$`

where

*s* is the semi-perimeter of the triangle

*a*,*b*,*c*, are the lengths of its sides.

Example 1:

For a triangle with side lengths a=5, b=12, and c=13. Find the area.

`${\text{s}}_{}=\frac{{\text{a+b+c}}_{}}{{\text{2}}_{}}$`

`${\text{s}}_{}=\frac{{\text{30}}_{}}{{\text{2}}_{}}$`

s = 15

`${\text{area}}_{}=\sqrt{15(15-5)(15-12)(15-13)}$`

Area = 30 square units

Example 2:

For a triangle with side lengths a=7, b=24, and c=25. Find the area.

`${\text{s}}_{}=\frac{{\text{a+b+c}}_{}}{{\text{2}}_{}}$`

`${\text{s}}_{}=\frac{{\text{56}}_{}}{{\text{2}}_{}}$`

s = 28

`${\text{area}}_{}=\sqrt{28(28-7)(28-24)(28-25)}$`

Area = 84.017 square units

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