How to determine the area of the circle in a Triangle

In this construction video tutorial you can learn how to determine the area of a circle that is provided in a triangle.

In the example given in the video, the sides of the triangle is given as a = 20 feet, b = 15 feet and c = 12 feet. Area is represented as A.

To find out the area, the following formula is applied :-

Here, the length of the steel is taken as 1 meter

Area = A = πR²
The radius of the circle is unknown.

The radius of the circle is determined with the following formula :-

A/P = R/2
Now multiply with 2 on both side 2 x A/P = 2 x R/2
R = 2A/P i.e. radius is the two times of Area.
P defines perimeter and it is determined by adding 3 sides of the triangle i.e. 20 + 15 +12 = 47 feet.

To find out the area, the following formula is used :-

The value of S determined as = S = a+b+c/2 = 23.5 feet

By putting the value of S, we get the following :-

A = 89.6657 Sft

Now Radius (R) can be easily found as :-

R = 2(89.6657)/47 = 3.815 ft.
Now, calculate Area (A) = πR2
We know the value of R as 3.815 ft.
So, Area (A) will be = π(3.815)2= 47.736 sft.

To learn the complete process, watch the following video tutorial.

Video Source: SL Khan