How to Find the Area and Perimeter of any Triangle?

How to Find the Area and Perimeter of any Triangle – A triangle is a three-sided closed polygon that also has three vertices and three angles. Before a child is introduced to Geometry, she needs to learn about various basic concepts such as lines, angles, triangles, and so on. In this article, we will be discussing the area of triangle formula, how to calculate the perimeter and the best way to study such a complicated topic.

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Area of a Triangle

The area of a triangle can be defined as the space enclosed by the three sides of that triangle. It can also be defined as the space occupied by a figure in two-dimensional space. There are three basic formulas that can be used to calculate the area of a triangle, as listed below.

1. Heron’s Formula

If the measure of all three sides of a triangle is known, then we can use this formula.

If we have a triangle with side lengths d, h, l, then the heron’s formula is given by

Area of a triangle =

Where the semi-perimeter of the triangle is represented by s and is given by

s = ( d + h+ l) / 2

2. Base height Formula

When we know the length of one side and drop a perpendicular in it from the opposite vertice giving us the measure of the height, then the Formula is given by

Area of a triangle = ½ (base)(height)

3. Trigonometric formulas

To use these formulas, you need to know the measure on two sides and the angle opposite to it.

If we have a triangle DHL with side lengths given d, h, l, and angles D, H, L, then you can find the area of the triangle by using any one of the formulas as listed below.

A(ABC)= ½ hl sin D
A(ABC)= ½ dl sin H
A(ABC)= ½ dh sin L

4. Law of Cosines

If you know the measure of two sides and also know the opposite angle, another way to find the area of a triangle is by using the law of cosines. We can find the length of the third side and then substitute these values in Heron’s Formula to get the answer. Taking into account the same triangle as mentioned above, suppose we know d, h, and L. Using the law of cosines, we get

l = d² + h² – 2dhcosL

We can then substitute the values of d, h, l in Heron’s Formula and get the area of the triangle.

Perimeter of a Triangle

The perimeter of a triangle can be defined as the sum of lengths of all three sides. Suppose we have a triangle DHL with side lengths d, h, l, then the perimeter is given by

Perimeter = Sum of all sides

= d + h + l

How to Study Triangles?

The best way to study a topic is by taking the help of a good and reliable tutorial such as Cuemath. At Cuemath, the certified tutors deliver an impactful lecture by using several resources such as worksheets, workbooks, online math games, interactive puzzles, etc. The focus is placed on developing a robust mathematical foundation, and good grades follow inevitably. They also ensure that a child follows his pace of learning so that he does not get stressed and can approach a topic with enthusiasm. Thus, you can avail the services of such an institution to master the subject in no time.