The total surface area of a rectangular prism is found by: 2(lw+lh+wh)=SA where l represents the length, w is the width, and h represents height.
Since we know the Base is a square that means that the length and width are equal values. Therefore to find each length and width, take the square root of 1296.
Length and Width both = `sqrt(1296)=36`
Therefore substituting these values in for the formula for surface area, solve for "h" to find the height.
SA = `2(36*36+36h+36h)`
`6048 = 2(1296+72h)`
`-2592 = -2592`
`3456 = 144h`
`Therefore, the height of the wooden block is 24 centimeters.`