![]() Here is another method for calculating the area of an equilateral triangle. Heron’s formula for the area of an equilateral triangle is Area = √(s(s-a) 3), where a is the side length.įor a triangle that has 3 equal sides, the semi-perimeter is simply s = 3a/ 2. 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. 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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