Sunday, 17 August 2008

How To Find Area Of Triangle (1)

Computing area of a specific shape is a necessary skill in mathematics. The concept in calculating the area is relatively simple if the principles of related maths topics are understood.

Examples of knowledge needed to find area of various shapes:

  • Trigonometry

  • Line of symmetry

  • Pythagorus' Theorem

  • Radian (angular measurement)

In this post, let us do a simple challenge.

Find the area of the below triangle ABC given the shown parameters.

Finding area of a triangle

The solution is given below. But try out yourself to see personally the other maths knowledge needed to handle this challenge.





To find the area of a triangle, we need to know the formula
triangle area = (1/2) x Base x Height

What is the "base" value of the triangle in question?

There are 2 methods to getting this "base" value.

Method 1 (Trigonometry skill)

Diagram 1

Using diagram 1, we can find the angle Y from the given length in the hypothenus and height.

cos Y = 1 / 2 ===> Y = cos -1 (1/2) = 600

Knowing the angle Y, we can now get the "base" of the triangle. How?

By applying the trigonometry function sin Y.

sin Y = sin 600 = P / 2 ==> Base of triangle, P = 2 x sin 600 = 1.732 unit

With this, we have found all the necessary information to compute the area!

Note the "P" is just the base of half the whole triangle ABC with the centre vertical line acting as the "Line of Symmetry".

We, therefore, need to know only the area of half the ABC triangle to obtain the whole ABC triangle area ( by multiplying by 2).

Area of triangle ABC = 2 x (1/2) x P x Height = P x Height
= 1.732 x 1 = 1.732 unit2

Simple? Yes! It must be. :)

Let's try the other method which is the Pythagorus' Theorem approach.

Method 2 (Pythagorus' Theorem)

From diagram 1, applying the Pythagorus' Theorem,
P2 + height2 = hypothenus2

P2 + (1)2 = (2)2

P2 = (2)2 - (1)2 = 4 - 1 = 3

P = Sqrt(3) = 1.732 unit P is the same as previous!

Area of triangle ABC = 2 x (1/2) x P x Height = P x Height
= 1.732 x 1 = 1.732 unit2

Again, isn't it simple?


2 methods to compute the area of the triangle are presented here to stress the flexibility in mathematics when you understand the application of certain principles in maths.


1 comment:

mr hesham said...

thank you for this post
area of shapes is very useful lesson
i like pick theorem to get area of any shape