Although there is no picture, I will assume this is a triangle we are talking about since the terms base and height are being used. If that is the case, the height is roughly 38.72in.
To find this, we will use the area of a triangle formula.
1/2bh = a ---> plug in known values. 1/2(12.6)(h) = 244 ---> multiply to simplify 6.3(h) = 244 ----> divide both sides by 6.3 h = 38.73