How to Calculate Area of a Triangle?

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How to calculate the area of a triangle is one of the basic mathematics that high school mathematicians are usually faced with. The perimeter of a triangle is actually basic as it only requires that simple addition. Fortunately, the Are of triangles is no different.

However, there is a basic difference: the area of a triangle employs both division and multiplication. Not to worry, though; it is very easy to calculate a triangle area irrespective of its shape and nature. This article will fully outline how to calculate the area of the most popular triangles.

Area of Triangle Formula

The Area of a Triangle is expressed in square centimetres as it requires the multiplications of more than one centimeter. The basic formula is

Area = ½ B x H

However, this is not the only formula, and this will be discussed in subsequent sessions.

How to Calculate the Area of a Triangle?

Since there are different Triangles, calculating their areas may require different types of formulas. There are numerous methods available. However, this article will consider three ways to perform their respective calculations as they are the most commonly used for computations.

The Basic Formula: ½ BXH

This formula is based on a normal triangle where there are two equally heights and a base. The base and height need to be available to use the formula. To calculate;

Step 1: multiply the base and height

Step 2: divide the multiplied base and height by 2

Example 1: Find the Area of the Triangle

Solution

Just as its name, the base is the bottom at 6cm while  the height is 4cm.

The formula is ½ BXH

Step 1: multiply the base and height

6cm x 4cm = 24cm2

Step 2: divide the multiplied base and height by 2

½ b x h = ½(24cm2) = 12cm2

The Area of a Right Angle Triangle

The formula for a right-angled triangle is the same area = ½ b x h. However, in most cases, the base or height may not be available for calculation. The side length is mostly available.

To find the base or height when the side length is available requires the use of Pythagoras’ Theorem
The Pythagoras Theorem computation is expressed as
B2 + H2 = SL2
Let us consider an example;
Solution
Now B =? H = 6, SL = 8
B2 + H2 = SL2
B2 + 62 = 82
B2 + 36 = 64
B2 = 64 – 36
B2 = 64-36 = 28
B = 5.29
Since the b and h are now available,
 Area = ½ B x H
Area = ½ (5.29 X 6)
Area = 15.87 cm2

Using Side Lengths

The Side length formula is another way of calculating the area of a triangle.

This formula is expressed as;

Where s = ½ (a + b + c)

How to calculate the area of a triangle using the Side length formula?

Step 1: Calculate S

Step 2: Calculate the Area

Example

Calculate the area of the triangle below using the Side length

 

Solution

Step 1: Calculate S

S = ½ (a + b + c)

S = ½ (5.29cm + 6cm + 8cm)

S = ½ (19.29)

S = 9.645

Step 2: Calculate the Area

Conclusion

Calculating the area of a triangle is very straightforward and, with appropriate computation, can only take a few minutes. Many students who already know how to calculate the perimeter of a triangle will find the method of calculating a triangle’s area very easy. While there are definitely different triangles, there are certain ways to ensure you have your answer.

This article has considered three different ways to compute the area of the triangle. Generally, these three methods will be sufficient irrespective of the type of triangle that you want to compute. This is because most triangles usually have at least two measurements of their sides available.

An important notice in this article is that all the computation was extremely easy. All the steps to calculate each process were outlined, and following them is very easy.

How to Calculate Area of a Triangle?

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