first break the shape up into component shapes. the shape is made of two rectangles and two triangles. the area for a rectangle is A=BH where b is base and h is height. the area of a right triangle is BH/2 where b is the base and h is the height. you are given the base and height of the top rectangle 4x7. To find the area of the triangles and the second rectangle you have to do some algebra. the total base length is 19cm and the top rectangle has a length of 7cm so 19-7 leaves you with 12cm to spare and there is two symmetric triangles on each side so 12/2 is 6. now we know all the measurements and can solve.
Since the score is the sum of all cards a player has, the way to make it smallest is to use the smallest cards. So the 7 smallest cards are 1, 2, 3, 4, 5, 6 and 7. So you want to add these up. This gets 28
