In this video I explain how to find the area of a segment in a circle. To understand how a segment is formed I begin by explaining what is meant by a sector of a circle and when a chord is drawn between the point where the sector intersects the circle, a segment is created. I also demonstrate that a triangle is created where the segment plus triangle make up the sector.
Armed with this knowledge I demonstrate that if the area of the triangle is subtracted from the area of the sector then we obtain the area of the segment.
I then use an example to find the area of a sector and demonstrate two methods for finding the area of a triangle. The first method uses the formula 1/2 x (base x height) and I create a 90° triangle by halving the sector angle and dropping a perpendicular until it meets the chord. I then use trigonometric functions and soh cah toa to find the lengths of the base and height of the triangle. The second method uses the formula 1/2 x a x b x Sin C where a and b are the known lengths of two sides of a triangle and C is the included angle SAS.
Having obtained the area of the triangle I then subtract this from the area of the sector to find the area of the segment.
Area of a sector of a circle in the link below
https://youtu.be/3OpeRAgJOrM