A point inside a pentagon is connected to the midpoints of the sides of the pentagon and to a corner, as shown in the figure. The areas of the six regions are written in the figure.
What is the value of A – B?
P is a point inside triangle ABC. Lines are drawn through P parallel to the sides of the triangle. The three resulting triangles with the vertices at P have areas 4, 9, 49 sq units. The area of triangle ABC is
A Greedy person is celebrating his birthday with 6 of his friends. His mother baked him a birthday cake in the shape of a regular hexagon. Wanting to keep most of the cake, he makes cuts linking the midpoints of every 2 adjacent sides, and distributes these 6 slices to his friends. What proportion of the cake does he have left for himself?
A square is in the first quadrant, as shown, with its sides extending to points on the x-axis of (3, 0), (5, 0), (7, 0) and (13, 0). What is the area of the square?
Rectangle ABCD is made up of 5 equal rectangles, as shown. Point E is on side CD, and AD = 10. What is the area of triangle ABE?
A boy started from one corner of a rectangular path and walks along the adjacent sides to reach opposite corner. If he had walked through a shortest distance diagonally, he could have saved the distance equal to five-sixth of the shortest side a park, then what is the ratio of a longest side to the shortest side?
