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Formula for area of a triangle
The area of a triangle is represented by its three sides. If a triangle has a perimeter of 14, the area is calculated by multiplying its three sides. It is equal to . With a radius of 6, the area is equal to .The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it. It is applicable to all types of triangles, whether it is scalene, isosceles or equilateral. To be noted, the base and height of the triangle are perpendicular to each other. The unit of area is measured in square units.
Now, let’s see how to calculate the area of a triangle using the given formula. The area formulas for all the different types of triangles like an area of an equilateral triangle, right-angled triangle, an isosceles triangle are given below. Also, how to find the area of a triangle with 3 sides using Heron’s formula with example.An equilateral triangle is a triangle where all the sides are equal. The perpendicular drawn from the vertex of the triangle to the base divides the base into two equal parts. To calculate the area of the equilateral triangle, we have to know the measurement of its sides.A right-angled triangle, also called a right triangle has one angle at 90° and the other two acute angles sums to 90°. Therefore, the height of the triangle will be the length of the perpendicular side. The area of a triangle with 3 sides of different measures can be found using Heron’s formula. Heron’s formula includes two important steps. The first step is to find the semi perimeter of a triangle by adding all the three sides of a triangle and dividing it by 2. The next step is that, apply the semi-perimeter of triangle value in the main formula called “Heron’s Formula” to find the area of a triangle.
The area of the triangle is calculated with the formula: A = 1/2 (base × height). Using the same formula, the height or the base can be calculated when the other dimensions are known. For example, if the area and the base of the triangle is known then the height can be calculated as, Height of the triangle = (2 × Area)/base. Similarly, when the height and the area is known, the base can be calculated with the formula, Base of the triangle = (2 × Area)/height.In a triangle, when two sides and the included angle is given, then the area of the triangle is half the product of the two sides and sine of the included angle. For example, In âˆ†ABC, when sides 'b' and 'c' and included angle A is known, the area of the triangle is calculated with the help of the formula: 1/2 × b × c × sin(A). For a detailed explanation refer to the section, 'Area of Triangle With 2 Sides and Included Angle (SAS)', given on this page.This method involves drawing a smallest box that will enclose the triangle. Make sure that the box follows the grid of the graph paper. The space between the triangle and box is subdivided into right triangles and rectangles and the total area of the space is calculated. The area of the required triangle is then the area of the space subtracted from the area of the box. (Source:www.onlinemathlearning.com)
Heron's formula is a special case of Brahmagupta's formula for the area of a cyclic quadrilateral. Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral. Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the quadrilateral to zero.
An isosceles triangle is a triangle whose two sides are equal and also two angles are equal. The formula for the area of an isosceles triangle is; A scalene triangle is a triangle with 3 different side lengths and 3 different angles. The area of a scalene triangle can be calculated using Heron’s formula.Raifaizen, Claude H. (1971). "A Simpler Proof of Heron's Formula". Mathematics Magazine. 44 (1): 27–28. (Source:en.wikipedia.org))