A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $$\frac{A}{3}$$ and the height is $$d$$, the capacitance of the arrangement is 

step 1: understand geometry

the bottom plate is flat (area A)
the top plate has 3 steps, each of area A/3

their separations from bottom plate are:

• lowest step → distance = d
• middle step → distance = 2d
• top step → distance = 3d

step 2: treat as capacitors

each step forms a capacitor with the bottom plate

all are connected in parallel (same two plates → same potential difference)

step 3: capacitance of each

$$C_1=\frac{\varepsilon_0(A/3)}{d}$$

$$C_2=\frac{\varepsilon_0(A/3)}{2d}$$

$$C_3=\frac{\varepsilon_0(A/3)}{3d}$$

step 4: total capacitance (parallel)

$$C=C_1+C_2+C_3$$

$$=\frac{\varepsilon_0A}{3d}\left(1+\frac{1}{2}+\frac{1}{3}\right)$$

$$=\frac{\varepsilon_0A}{3d}\cdot\frac{11}{6}$$