How to determine the area of the circle in a Triangle
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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
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