Sunday, 17 August 2008

How To Find Area Of Triangle (2)

Triangles come in many form. Some are right-angled, some are not. And to determine the area of these triangles requires method that may vary with the type of triangle in question.

The area of the right-angled triangle is the easiest to find though. Click this link to see the simplicity in calculating it.

Let's look at the below triangle and study how to get its area.

Diagram A

To find the area of the triangle in diagram A, it will not be simply the application of the area formula (1/2) x Base x Height. It requires some technique.

What is the technique? Nothing difficult but some simple steps and logic.

The triangle of diagram A can be re-drawn as diagram B (below).

Diagram B

Diagram B is re-drawn to demonstrate the method to solve the area.

  • To get the area of the triangle, we need to find the area defined by the boundary PQRS, a bigger triangle.

  • Next, we need to determine the area defined by PQR.

  • By subtracting the above 2 areas, we will get the area of the desired triangle PRS.

Area of triangle PQRS = (1/2) x (3 cos 500 + 2) x (3 sin 500) = A1
Area of triangle PQR = (1/2) x (3 cos 500) x (3 sin 500) = A2

Therefore, A1 - A2 = area of triangle PRS = 3 sin 500 ANSWER.

The technique is simple, right?

The trick to solving this type of question is to first analyze the diagram and see what information can be obtained, before determining the area.


Next, we arrived at the question,

"Why do we need to calculate area of triangle?".

The pictures below self-explain the reason.

These shapes require the knowledge of the triangular area (or its parameter) to generate the plate and profile.


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