Measurement is the process or the result of determining the ratio of a physical quantity to a unit of measurement. The science of measurement is called metrology. There are many different forms of things that we can measure like time, length, height, size, temperature, mass etc. The dimension, quantity, or capacity is determined by its measurement. Measurement is used in our daily lives for example; when you want to buy a house, you need to defy it by its dimension and size.
Mensuration in its literal meaning is to measure. It is generally used where geometrical figures are concerned. Where one has to determine various physical quantities such as area ,volume ,length, measuring these quantities is called mensuration, also it is used where quantities like speed ,velocity and acceleration etc are concerned. Mensuration is divided into two parts; plane mensuration and solid mensuration. Plane mensuration deals with the measurements of solids, perimeters and areas of plane figures like triangle, polygons etc. Solid measurements deals with measurements of surfaces, areas and volumes of solid figures like cube, cuboid, sphere, cone, cylinder etc. :)