If the three sides of a triangle are given as 3, 5 and 7, its area can be calculated with the formula, area = √. What is the Area of a Triangle with Sides 3, 5, 7? For example, if two sides of a triangle are 5 units and 7 units and the included angle is 60°, then, Area = (7 × 5 × sin 60)/2 = 15.15 square units. This is also known as the "side angle side " method. If the sides of a triangle are given along with an included angle, the area of the triangle can be calculated with the formula, Area = (ab × sin C)/2, where 'a' and 'b' are the two given sides and C is the included angle. What is the Area of a Triangle with three Sides and an Angle? For example, if the height (altitude) of a triangle = 8 units, and the side of the triangle on which the altitude is formed is given (base) = 7 units, we can find its area using the formula, Area of a triangle = 1/2 × base × height. 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. Therefore, for the three angles to total 180º, the third angle must be 110º.In order to find the area of triangle with 3 sides, we use the Heron's Formula. The child would need to work out that the two angles shown equal 70º. They may be given a diagram like this (not drawn to scale): They are taught that the internal (inside) angles of a triangle always total 180º. (If we didn't divide by 2 we'd be calculating the area of a rectangle, represented below by the total green area.)Ĭhildren in Year 6 also move onto finding unknown angles in triangles. We multiply these to make 24cm and then divide this by 2 to make the area which is 12cm². This means that you multiply the measurement of the base by the height, and then divide this answer by 2.įor example, this dark green triangle has a base of 6cm and a height of 4cm. There is a basic formula for this, which is: In Year 6, children are taught how to calculate the area of a triangle. In Year 5, children continue their learning of acute and obtuse angles within shapes. A right-angled triangle has an angle that measures 90º.
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