A) It looks like the [irregular] hexagon has 3 rectangles and 2 triangles within it. So let's exclude the triangular corners on bottom left and top right for now. First we have a large rectangle covering most of the upper left of the polygon. 20 ft × 7 ft = 140 sq.ft. Now we have a rectangle on the bottom right. The width is 11 ft, so take the 7 away from that, 4 ft. × 14 ft. on bottom. 4 ft × 14 ft = 56 sq.ft. The last small rectangle fits on the right between the 2 other rectangles. It is 24-20 on top/bottom × 7-6 right/left. 4 ft × 1 ft = 4 sq.ft. Now for the triangles: bottom left is 11-7 × 24-14 = 4 ft × 10 ft. 1/2bh = 1/2×10×4 = 20 sq.ft. Top right is 24-20 × 11-5 = 4 ft × 6 ft. 1/2bh = 1/2×4×6 = 12 sq.ft.
B) Add them all together for the total area (A): A = 140 + 56 + 4 + 20 + 12 = 140+60+32 = 232 sq.ft.
Then the experimental probability of rolling a number greater than four would be 36 or one-half. As the number of trials increases, the experimental probability will become close to the theoretical probability.
