In the adjoining figure, two rectangles and two right-angled triangles are arranged as shown. The numbers shown inside each are their respective areas. Then the area of $$A$$ is

Let the left and right widths be $$w_1,w_2$$ and the upper and lower heights be $$h_1,h_2$$. The given regions give $$w_1h_1=72$$, $$\frac{1}{2}w_2h_1=48$$ and $$w_2h_2=128$$. Hence $$w_1h_2=\frac{(w_1h_1)(w_2h_2)}{w_2h_1}=\frac{72 \times 128}{96}=96$$. Therefore, $$A=\frac{1}{2}w_1h_2=48$$.