\( \begin\)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. To Construct a Triangle whose Three Sides are given.In order to find the area of triangle with 3 sides, we use the Heron's Formula. (vi) A triangle with unequal sides is called a ……………………… (v) A triangle whose 2 sides are equal is called a ……………………… (iv) A triangle with all sides equal is called a ……………………… (iii) A triangle can be classified on the basis of ……………………… (i) A triangle is ……………………… sided polygon. (e) A triangle can have two obtuse angles. (d) Equiangular triangle has its three sides also equal. (b) If one angle of a triangle is obtuse, the other two angles must be acute. (a) All the angles of an isosceles triangle are equal. Find the other acute angle.ġ6. Say whether the following statements are true or false: What kind of triangle is this?ġ5. One of the acute angles of a right triangle is 48°. Find the length of its third side.ġ4. Each side of a ∆ is one third of its perimeter. Determine the other angles.ġ3. The perimeter of a triangle is 24 cm. Find the measure of each angle of the triangle.ġ2. One of the two equal angles of an isosceles triangle measures 55°. Measure its sides andĬlassify the triangle as Isosceles triangle, scalene triangle or equilateralġ1. The angle of a triangle is in the ratio of 2: 3: 4. (e) 50°, 50°, 90° (f) 10 cm, 12 cm, 2 cm.Ĩ. Find the perimeter of a triangle when its sides are: (f) 3.5 cm, 3.5 cm, 4.5 cm.ħ. Is it possible to have a triangle with the following angles and sides? Give reason in support of your answer. Classify the triangle according to sides, that is, equilateral, isosceles and scalene triangles
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