The area of an equilateral triangle can be calculated using the formula, Area = a 2(√3/4), where 'a' is the side of the triangle. If a triangle has 3 equal sides, it is called an equilateral triangle. 's' be calculated as follows: semi perimeter = (a + b + c)/2 What is the Area of Triangle with 3 Sides Equal Sides? The area of a triangle with 3 sides can be calculated with the help of the Heron's formula according to which, the area of a triangle is √, where a, b, and c, are the three different sides and 's' is the semi perimeter of the triangle. \( \begin\)įAQs on Area of Triangle with 3 Sides What is the Area of a Triangle With 3 Sides? Using one of the Trigonometric identities, Using law of cosines, cos A = (b 2 + c 2 - a 2) / 2bc. The proof of the formula for the area of triangle with 3 sides can be derived in the following way.Ĭonsider the triangle shown above with sides a, b, c, and the opposite angles to the sides as angle A, angle B, angle C. How to Find Area of Triangle with Three Sides? Proof of Area of Triangle with 3 Sides Formula This formula was derived by a Greek mathematician known as the Heron of Alexandria. However, if the altitude of a triangle is not known, and we need to find the area of triangle with 3 different sides, the Heron's formula is used. The basic formula that is used to find the area of a triangle is ½ × Base × Height where "Base" is the side of the triangle on which the altitude is formed, and "Height" is the length of the altitude drawn to the "Base" from its opposite vertex. The area of a triangle can be calculated with the help of various formulas. Using this, the area of a triangle (A) with 3 sides a, b, and c is calculated using the formula A = √, where 's' is the semi-perimeter of the triangle given by s = (a + b + c)/2. Many of these problems take more than one or two steps, so look at it as a puzzle and put your pieces together!īelow you can download some free math worksheets and practice.In order to find the area of triangle with 3 sides, we use the Heron's Formula. If you don’t remember that last step, don’t worry! You can just take two more steps and find the 3 rd angle of the bottom triangle and subtract it from 180°to find the exterior angle. We need a few pieces of the puzzle before we can find the measure of x. They ultimately want to find the measure of that exterior angle. There’s actually at least three different ways that you can answer this problem. Find a piece at a time and put them together until you reach your answer! You have to look at these problems as “puzzles” because sometimes you need to find a part that they are not asking for in order to find the final result. Let’s see if we can put these properties to work and answer a few questions. So, in EVERY equilateral triangle, the angles are always 60°. This is because all angles in a triangle always add up to 180°and if you divide this amongst three angles, they have to each equal 60°. The angles, however, HAVE to all equal 60°. The sides can measure anything as long as they are all the same. When all angles are congruent, it is called equiangular. In an equilateral triangle, all sides are congruent AND all angles are congruent. Here are some diagrams that usually help with understanding. Since two sides are congruent, it also means that the two angles opposite those sides are congruent. Well, some of these types of triangles have special properties!Īn isosceles triangle has two sides that are congruent. We’ve learned that you can classify triangles in different ways.
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