A polygon that has three sides, three angles, and three vertices joined end to end is known as a triangle. Triangles form an integral part of mathematics are they find use in several topics such as geometry, trigonometry, surface areas, and volumes, etc. However, before moving on to tougher topics, we have to start our study of triangles by learning how to find the area of triangle with 3 sides. In this article, we will cover several aspects associated with triangles, including important properties, types, and how to find the area.
Properties of Triangles
There are several questions that not only require the application of formulas related to triangles but also need students to know about the various properties associated with helping them to manipulate and simplify the problems at hand.
1. A triangle will only have three sides, three edges, and three angles.
2. The sum of all the angles of a triangle, also known as the internal angles, is equal to 180 degrees. This is known as the angle sum property.
3. The sum of the lengths of any two sides of a triangle is always greater than the third side. The difference between any two sides is always lesser than the measure of the third side.
4. The smallest interior angle of a triangle is opposite the shortest side. Similarly, the largest angle of a triangle is opposite the longest side.
5. The exterior angle of a triangle is equal to the sum of the opposite interior angles. This is also known as the exterior angle property.
Types of Triangles
Based on Sides
1. Equilateral Triangle
All sides are of the same length.
2. Isosceles Triangle
Only two sides are of the same length.
3. Scalene Triangle
All sides are of unequal length.
Based on Angles
1. Acute Angled Triangle
The measure of all sides is less than 90 degrees.
2. Right Angled Triangle
One angle measures 90 degrees.
3. Obtuse Angled Triangle
One angle is greater than 90 degrees.
Area of a Triangle
The space enclosed by all three sides of a triangle is called the area of a triangle. The following methods can be used to calculate the area of any triangle.
- Heron’s Formula
If we have a triangle with side lengths e, f, d, then the heron’s formula is given by
Area of a triangle =
where s stands for the semi – perimeter of the triangle and is given by
s = ( e + f + d) / 2
- Base height Formula
When we know the length of one side and drop a perpendicular in it from the opposite vertice forming the height, then the formula is given by
Area of a triangle = ½ (base)(height)
- Trigonometric formulas
If we have a triangle ABC with side lengths given by a, b, c, and angles A, B, C, then you can find the area of the triangle by using any one of the formulas as listed below.
- A(ABC)= ½ bc sin A
- A(ABC)= ½ ac sin B
- A(ABC)=½ ab sin C
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