Assuming the shape is a piece of a circle, you can determine the ratio of the shape to a full circle. A full circle will have 360 degree but this shape is only 40 degree. Then the ratio would be: 40/360= 1/9 full circle.
Then, using the circle area formula, the area of the 1/9 circle would be: full circle area= pi * r^2 full circle area= 22/7 * 6^2 full circle area= 792/7 1/9 full circle area= 792/7*9= 88/7 = 12.57
