She is correct, first of all, to add 7/8 and 5/6; you must have common denominators so make 7/8 into 42/48 and make 5/6 into 40/48. Then just add them together now, and it will be 82/48. This when you divide 82/48 it will be 1 17/24. So, your answer is, yes, Kit is right.
Please comment on this so I can see the full question
The pentagon's area is the sum of the 5 triangles that comprise it. This is

where the factor of 2 accounts for the top and bottom. The walls have an area of 5 rectangles