Diagonals d1 and d2 cross perpendicularly. (i) Algebraically, the kite splits into two triangles on base d1 with heights summing to d2, giving area (1/2)d1d2. (ii) Geometrically, enclosing it in a d1 x d2 rectangle doubles its area.
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The trapezium is split into a parallelogram of base a and a triangle of base (b – a), both sharing height h. Area = ah + (1/2)(b – a)h = (1/2)(2a + b – a)h = (1/2)(a + b)h.