3. Let P be a parallelogram with vertices at (0,0), (a, b), (a + c, b + d), and (c, d), oriented counter- clockwise. This means that the inside of the parallelogram is to the left as you walk around the perimeter according to the order of the vertices above, see Figure 2. Prove that the area of P is ad be by cutting P into pieces and reassembling them into a rectangle, as in Figure 3. (For simplicity assume that a, b, c, d 2 0 so that the pictures below are accurate.) Also prove that the area of the triangle with vertices at (0,0), (a, b) and (c, d) is %(ad bc). (a+c,b+d) (c, d) (a, b) (0, 0) Figure 2: A parallelogram. g Figure 3: Idea for a proof of the formula for the area of a parallelogram with vertices at (0,0), ((1, b), (a | c, b + d), and (c, d), where a, b, c, d > 0. The rst, third, and fth parallelograms have the same area. The lower left vertex is at (0, 0) in all the gures. What are the sides of the nal rectangle? (c, d) ('11 b) (01 0)