Muhammad's Dissection

Let $A_1B_1C_1D_1A_2B_2C_2D_2$ be a unit cube, where the vertex $X_2$ is vertically above the vertex $X_1$ . Let $M$ be the center of face $A_2 B_2 C_2 D_2$ . Rectangular pyramid $MA_1B_1C_1D_1$ is cut out of the cube. The surface area of the solid that remains after the pyramid is removed is expressed in the form $a + \sqrt{b}$ , where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. What is $a+b$ ?

This problem is posed by Muhammad A.