amitkmr988

· 04 Jan 2022

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How to find the area of a triangle?

What is a Triangle?

Let me tell exactly what my teacher taught me in high school. He said, a Triangle in a simple term is defined as a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

Features of a Triangle

•    Perimeter: sum of side lengths of the triangle
•    Number of vertices
•    Number of edges
•    Internal angle
•    Sum of interior angles: 180°
•    Line of symmetry

Finding the area of a triangle

We will use different method to find the Area of a triangle.
1. Using Trigonometry
You can find the area of a triangle if the length of two adjacent sides and the included angle are given.  Adjacent sides are two sides of a triangle that meet at a vertex. The included angle is the angle between these two sides.
Example, you might have a triangle with two adjacent sides measuring 15 cm and 23 cm in length. The angle between them is 123 degrees.

Set up the trigonometry formula for the area of a triangle.

The formula is Area = (bc/2) x sine A
Where A =123°
Therefore, Area = (15 x 23/2) x sine (123)
Area = 172.5 x sine (123)
Area = 172.5 x 0.83867
Area = 144.671cm²
2. Using the Half Base times height Formula
This method is mostly used to find the area of a right-angle triangle.  The base is one side of the triangle. The height is the measure of the tallest point on a triangle. It is found by drawing a perpendicular line from the base to the opposite vertex.

For example, you might have a triangle with a base measuring 5 cm long, and a height measuring 3 cm long.

Therefore, Area, A = 1/2 (base x height)
A = 0.5 x 5 x 3
A= 0.5 x 15
A = 7.5cm²

3. Find the area of an equilateral triangle.

A equilateral Triangle is such that has the length of all sides equal
Example of the length of each side of an equilateral triangle equals 6cm
Therefore,
Area of the triangle A = S² (√3/4)
S = length of one side of the triangle.
A = 6² x (√3/4)
A = 36 x (0.43301)
A = 15.59cm²

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