The solution depends on the information supplied.
Basically, you find the area of the sector containing the segment and then deduct the area of the triangle formed by the chord and the two radii enclosing the sector.
If you are given the radius(r) of the circle and the height(h) then construct a radius that is perpendicular to and bisects the chord. This will create two congruent triangles which together form the main triangle. Using Pythagoras enables the half-chord length to be calculated as the hypotenuse is r and the height (also the length of the third side) is r-h. With this information the full chord length can be established and thus the area of the main triangle. Using sine or cosine methods enables the sector angle at the centre to be calculated and thus the sector area. Simple subtraction produces the area of the segment.
If you are given the radius and the chord(c) length then the construction referred to above enables the height of the main triangle to be calculated and a similar process will generate the area of that triangle and the sector area. This, in turn, will enable the segment area to be determined.
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To find the angle of a triangle within a circle segment, you first need to determine the central angle of the circle segment. Then, you can use the properties of triangles inscribed in circles to find the angle. The angle of the triangle within the circle segment will be half the measure of the central angle.
To find the area of the circle pi*radius*squared and subtract the area of the figure inside
A segment of a circle is an area enclosed by a chord and an arc.
The segment is called a secant.The area bounded by a secant and its arc is a sector.
Area of a circle = pi*radius2