A triangle is a polygon with three sides and three vertices. It is the most basic geometrical shape. A triangle forms three angles at the three vertices. A triangle with three vertices as A, B and C is represented as ∆ABC. This article on how to calculate area of a triangle will help you in calculating area of a triangle in three different methods.
There are many methods for calculating area of a triangle. This article describes three methods for calculating area of a triangle. Area of a triangle is represented in square units.
Method 1:
The first method of calculating area of a triangle is very simple and is the most used method. The formula for calculating area of a triangle using this method is given as,
Area of a triangle = (1/2) b × h
In the above formula,
- “b” is the base of the triangle
- “h” is the height of the triangle
To calculate area of a triangle using this method you need to know the length of the base of the triangle and the length of height of the triangle.
- The height of the triangle is the perpendicular height. While calculating the area of triangle, you need to draw a perpendicular on one of the sides of the triangle considering it as the base of the triangle.
- If you have a right angled triangle than you need not draw a perpendicular on the base of triangle. You can simple measure the length of this perpendicular segment as the height of the triangle.
- Consider the side that is adjacent to this perpendicular and is making an angle of 900 as the base of the triangle.
- Before drawing the perpendicular you need to take a look at the triangle. Sometimes simply looking at the triangle you can identify whether it is a right angled triangle or not.
- If you are not confident, use a protractor to measure the angles of the triangle.
- Place the measured values of base and height in the above formula and calculate area of a triangle.
Example:
Suppose the length of base of a triangle is 4 cm and the length of height of a triangle is 5 cm and you have to measure area of that triangle.
Using the above formula,
Area of a triangle = (1/2) b × h
= (1/2) 4 × 5
= 10 cm2
Method 2:
The second method of calculating the area of triangle can be used if you know the coordinates of the triangle. Using this formula you can directly use the coordinates of the triangle instead of using the measurements of sides of the triangle.
The formula for calculating area of triangle using this method is,
Area of a triangle = (xB - xC) × (yA - yC)/2 – (xA - xC) × (yB - yC)/2.
While using the above formula to calculate area of a triangle, sometimes the value may come negative depending upon the coordinates of the triangle, so we need to take the absolute value of the area of the triangle.
Area of a triangle = abs ((xB × yA - xA × yB) + (xC × yB - xB × yc) + (xA × yC - xC × yA))/2
We know that the triangle has three vertices. Let the three vertices of the triangle be A, B and C. Then, A = (xA, yA), B = (xB, yB), C = (xC, yC) are the coordinates of the vertices of the triangle.
- If you have got a graph paper then, draw a triangle on the graph paper and note down the values of the co-ordinates of the triangle.
- If you already have a triangle drawn on the graph paper then simply note down the values of the vertices.
- You can also measure the area of a triangle without drawing the triangle on the graph paper if you know the values of the coordinates of the vertices of the triangle.
- Place the known values in the above formula and calculate the area of the triangle.
Example:
Suppose a triangle of vertices A, B, C has the values of coordinates as A = (4, 3), B = ( -2, 4 ), C = (-1, 3) and you have to calculate the area of the triangle.
Then simply put the values of the coordinates in the above formula. The values of coordinates are as follows,
- xA = 4 and yA = 3
- xB = -2 and yB = 4
- xC = -1 and yC = 3
Area of triangle = abs ((xB × yA - xA × yB) + (xC × yB - xB × yc) + (xA × yC - xC × yA))/2
Therefore,
Area of triangle = abs (((-2) × 3 – 4 × 4) + ((-1) × 4 – (-2) × 3) + (4 × 3 – (-1) × 3))/2
Area of triangle = abs (-24 + 2 + 15)/2
Area of triangle = abs (-7)
Therefore,
Area of triangle = 7 cm2
Method 3:
This method can be used to calculate area of an equilateral triangle. An equilateral triangle is the triangle in which the measure of all the three angles is 600.
The formula for calculating area of an equilateral triangle is given as,
Area of an equilateral triangle = (√3 × s2)/4
In the above formula, “s” is the measure of the side of the triangle.
- Measure the length of one of the side of the triangle and multiply it by √3.
- Divide the obtained value by 4 and you will get the area of the equilateral triangle.
Example:
Suppose the value of side of a triangle is 6 m whose angles are of equal measure and the sum of the angles is 1800 and you want to calculate the area of the triangle.
The sum of the angles is 1800 and all the angles are of equal measure. Therefore measure of each angle is 600 i.e. the triangle is an equilateral triangle.
Therefore,
Area of an equilateral triangle = (√3 × s2)/4
= (√3 × 62)/4
= 36√3/4
= 1.732 m2
You can use any of the above methods depending upon the data available with you and calculate area of a triangle.
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