Teaching Kids Programming – Geometry of Triangle Area and Side Law

Teaching Kids Programming: Videos on Data Structures and Algorithms

How to compute the area size of Triangle from Parallelogram/Rectangle

We know the area of triangle can be computed as the half of one side multiplied by the height of it. This can be seen from the above – the rectangle area is a * b where a and b are the length of two sides. And a Parallelogram can be transformed from a corresponding rectangle by cutting a piece and put it on the otherside. The triangle is half of a parallelogram.

The question of today is to compute the area of the following:

Compute the area inside a triangle given other parts are known

Geometry of Triangle Area and Side Law

Given a Triangle ABC, if we pick a point at side BC and make it D, AD divides the triangle into two parts, the left triangle ABD and right triangle ADC.

Geometry of Triangle Area and Side Law

We know the area of ABD is BD*AH/2 where AH is the corresponding height to the side BD.

Triangle Law

Also, the area of ADC is DC*AH/2.

Thus we have

S(ABD) to S(ADC) is equal to BD to DC as the common factors AH and 2 are cancelled out.

Let’s look at this triangle again. We split the unknown area by two namely x and y.

Compute x+y in Triangle

Then, we have:

and

based on above law, the equations are established because the Area Ratio is equal to the ratio of two common edges.

Then, two equations two unknowns, we can solve for x and y, and the answer is x+y.

In theory, we can apply Monte-Carlo simulation to randomly generate points and count the number of the points that fall into the area of (x+y). However, it might be tricky to test whether the random point falls in the area.

–EOF (The Ultimate Computing & Technology Blog) —