How do I find the area of a part of a circle enclosed by the circumfernce and a chord?

Question

I know the diameter is 12 and the chord length is 6. Thanks.

Answer 1

the cord and the radii drawn to its extremes form an equilateral triangle.
The remaining part of the circle has an area of pi*36*300/360
and the triangle has an area of 6*6sqrt(3)/4 = 9*sqrt3
Substract the sum of those areas from the area of the circle=
36pi and you get
36pi-30pi-9*sqrt3 = 6pi-9sqrt3 =3.2611

Answer 2

Draw the situation. Draw in a radius from the each end of the chord to the centre and a line from the centre to the mid-point of the chord which will be at 90 degrees. You do a trig. calculation on the right-angled triangle to find the angle at the centre. This is used to find the area of the sector. The area you want is the sector area subtract the area of the triangle.