![]() We will first look at finding the area of an equilateral triangle using Heron’s formula. Alternatively, Heron’s formula for an equilateral triangle is Area = √(s(s-a) 3), where a is the side length and s = 3a/ 2.Īn equilateral triangle is a triangle with 3 equal side lengths. The area of a triangle with 3 equal sides can be calculated with the formula Area = √3/ 4 a 2, where a is the length of one of the sides. How to Calculate the Area of a Triangle with 3 Equal Sides This is the same answer as before and either method can be used. ![]() This becomes Area = √35, which equals 5.92 cm 2. Here is an example of using the isosceles version of Heron’s formula: Area = √s(s-a) 2(s-b). 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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