The advantage of Heron’s formula is that no other lengths or angles of the triangle need to be known. Heron’s formula allows us to calculate the area of a triangle as long as all 3 of its sides are known. The formula is named after Heron of Alexandria (10 – 70 AD) who discovered it. It can be used to calculate the area of any triangle as long as all three side lengths are known. Heron’s formula is Area = √( s(s-a)(s-b)(s-c) ), where a, b and c are the three side lengths of a triangle and s = (a + b + c) ÷ 2. This becomes Area = √(10 × 2 × 7 × 1), which simplifies to Area = √140.įinally, the square root of 140 is calculated using a calculator. We find the semi-perimeter by adding up the side lengths and dividing by 2.Ĩ + 3 + 9 = 20 and 20 ÷ 2 = 10. The semi-perimeter is simply half of the perimeter. The first step is to work out the semi-perimeter, s. It does not matter which sides are a, b or c. Substitute the values of s, a, b and c into the formula of Area = √( s(s-a)(s-b)(s-c) ).įor example, find the area of a triangle with side lengths of 8 m, 3 m and 9 m.The steps to find the area of a triangle with 3 sides (a, b and c) are: Simply find the values of s, a, b and c and substitute these into the formula for the area. Heron’s formula is Area = √( s(s-a)(s-b)(s-c) ), where a, b and c are the 3 side lengths of the triangle and s = ( a + b + c) ÷ 2. To calculate the area of a triangle with 3 known sides, use Heron’s Formula. How to Calculate the Area of a Triangle with 3 Known Sides
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