![]() Here is an example of using the isosceles version of Heron’s formula: Area = √s(s-a) 2(s-b). This becomes Area = √35, which equals 5.92 cm 2. The semi-perimeter is the sum of the sides divided by 2.Ģ + 6 + 6 = 14 and 14 ÷ 2 = 7. We can use the usual form of Heron’s formula to find the area. Heron’s formula for an isosceles triangle then becomes Area = √( s(s-a) 2(s-b) ), where a is the length of the two equal sides, b is the length of the other side and s = (2a + b) ÷ 2.įor example, here is Heron’s formula for an isosceles triangle with side lengths of 2 cm, 6 cm and 6 cm. For an isosceles triangle, two sides are the same length and we can say that side c = side a. Heron’s formula for any triangle is Area = √( s(s-a)(s-b)(s-c) ). Heron’s Formula for an Isosceles Triangle As long as the three side lengths are known, Heron’s formula works for all triangles. 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.
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