Here in this article, we are talking about Triangles. As you know that, There are three sides and three vertices of a polygon that are interconnected to each other are known as a triangle. There are several topics associated with triangles, such as trigonometry, Pythagoras theorem, surface areas, and volumes, etc. Thus it is necessary for students to understand the basic concepts of triangles. For example – how can you calculate the area and perimeter of a triangle. Here, we will go through these concepts as well as the classification of triangles.
The perimeter of a Triangle
The basic things that you should know. It can be defined as the total length of the boundary of the triangle. As per this definition, we can say that the perimeter of a triangle is equal to the sum of lengths of the 3 sides. Suppose we have a triangle with vertices at A, B, and C. Then it has side lengths as AB, BC, and AC. In such a case, the formula for the perimeter is given as follows:
Perimeter of a triangle = addition of the three sides = AB + BC + AC
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Area of a Triangle
In simple words, the area of a triangle can be easily defined as the region enclosed by the boundaries of that triangle. There are some different methods that can let you calculate the area of a triangle depending upon which triangle is being dealt with. We will first look at a generalized formula to calculate the area of a triangle. This formula is referred to as Heron’s formula.
If we have a triangle with the lengths of the sides given by m, n, and o, then Heron’s formula is given by:
A = s (s – m) (s – n) (s – o) where s stands for the semi-perimeter of the triangle and is given by:
s = ( m + n + o) / 2
This formula can be applied to any triangle whose sides are known.
Suppose we have a triangle whose length of the height and base are known. In such a case, the area of a triangle is given by the following formula:
Area of a triangle = ½ (base) (height)
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Properties of Triangles
For simple questions, you might just be required to substitute the values in the given formulas; however, for complicated problems, you might have to use certain manipulations based on the properties of triangles. Thus, it is good practice to understand each property with clarity.
- All triangles have only three sides and three angles.
- The sum of all the interior angles in a triangle is always equal to 180 degrees.
- The sum of all the interior angles in a triangle is always equal to 360 degrees.
- The sum of the lengths of two sides of a triangle is always greater than the third side, while the difference is always lesser than the third side.
- The smallest interior angle is always opposite the shortest side, while the largest angle is opposite the longest side.
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Classification of Triangles
Based on Sides
- Equilateral Triangle – all sides are equal length.
- Isosceles Triangle – only two sides are of equal length.
- Scalene Triangle – all the sides are of unequal length.
Based on Angles
- Acute Triangle – all the angles are less than 90 degrees.
- Right Triangle – one of the angles of the triangle measures 90 degrees.
- Obtuse Triangle – one angle of the triangle is greater than 90 degrees.
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If you have clear concepts, then you will be able to master all concepts related to triangles. The simple method to do so is by joining a reliable online educational platform such as Cuemath that provides an outstanding quality of education to students. They combine fun with studies ensuring that a student has a strong foundational understanding of the topic.
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