Area of a triangle = 1/2 × base × height. If we know the sides of a triangle along with its height, we can use the basic formula for the area of a triangle. What is the Area of Triangle with 3 Sides and Height? For example, if an equilateral triangle has a side of 6 units, its area will be calculated as follows. 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. Our calculator provides answers almost instantly, making it much faster to solve multiple problems.In order to find the area of triangle with 3 sides, we use the Heron's Formula. Regardless of the type of triangle (scalene, isosceles, acute, or obtuse), our calculator will help you. Our calculator uses advanced algorithms to guarantee accuracy every time, giving you confidence in the results.īuilt with user preferences in mind, our platform makes it easy to solve triangles, even for people new to geometry. They provide insight into the properties of triangles and provide fundamental knowledge for more complex geometric concepts and real-world applications. Understanding and applying these facts, theorems, and laws is critical to anyone who studies geometry. Exterior Angle: An exterior angle of a triangle is equal to the sum of the two opposite interior angles.Īrea Calculation: The area $$$A $$$ of a triangle with the side $$$b $$$ and the height $$$h $$$ dropped to this side can be found using the following formula: $$A=\frac $$.Angle Sum: The sum of the interior angles of any triangle is always 180 degrees.What Are Some Key Facts, Theorems, and Laws Related to Triangles? Triangles are fundamental shapes in geometry and have various properties and theorems associated with them. Right-Angled Triangle: One of the angles is exactly 90 degrees, making it a right angle.Obtuse Triangle: One of the angles is greater than 90 degrees.Acute Triangle: All three angles are less than 90 degrees.Scalene Triangle: All sides have different lengths and all angles have different measures.
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