P is a point in the rectangle ABCD (as shown in the figure). The area of the triangle PAB is equal to 5, and the area of the triangle PBC is equal to 13. Q: what is the area of the triangle PBD?

P is a point in the rectangle ABCD (as shown in the figure). The area of the triangle PAB is equal to 5, and the area of the triangle PBC is equal to 13. Q: what is the area of the triangle PBD?

As shown in the figure, ① + ③ = ② + ④, so ③ - ④ = ② - ① = 13-5 = 8, so (③ - ④) + (② - ①) = 8 + 8 = 16, (③ - ④) + (② - ①) = (③ + ②) - (① + ④) = 12 (rectangular ABCD + △ PBD) area - 12 (rectangular ABCD - △ PBD) area = △ 2pbd area, so 2 △ PBD area = 16; △ PBD area = 8; answer: PBD area is 8