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Area of a triangle

# Area of a triangle

Did you know that there are three possible areas found when dividing a circle in half? These three areas are called the lateral, superior, and inferior triangles.In order to find the area of triangle with 3 sides, we use the Heron's Formula. The area of a triangle can be calculated with the help of various formulas. 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. 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. This formula was derived by a Greek mathematician known as the Heron of Alexandria. Let us explore the different formulas that are used to find the area of a triangle with 3 sides.

## HEIGHT

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 The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h. This formula is applicable to all types of triangles, whether it is a scalene triangle, an isosceles triangle, or an equilateral triangle. It should be remembered that the base and the height of a triangle are perpendicular to each other.

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 As in the proof of the law of sines in the previous section, drop a perpendicular AD from the vertex A of the triangle to the side BC, and label this height h. Then triangle ACD is a right triangle, so sin C equals h/b. Therefore, h = b sin C. Since the area of the triangle is half the base a times the height h, therefore the area also equals half of ab sin C. Although the figure is an acute triangle, you can see from the discussion in the previous section that h = b sin C holds when the triangle is right or obtuse as well. Therefore, we get the general formula (Source: www2.clarku.edu)

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